Titanium alloy mechanical property prediction method based on active learning

Abstract

This application relates to a method for predicting the mechanical properties of titanium alloys based on active learning. The method includes: acquiring a historical sample vector set, where each historical sample vector includes historical composition and process parameter components and labeled mechanical property components; analyzing the physical relationships represented by the historical composition and process parameter components based on the historical sample vector set to obtain physical relationship data; wherein the physical relationship data includes a physical coupling matrix and a parameter causal relationship graph; constructing a physical manifold encoder based on the historical sample vector set; initializing a Gaussian process regression model to obtain an initial prediction model, and training the initial prediction model based on a preset candidate sample vector set, physical relationship data, and physical manifold encoder to obtain a trained titanium alloy mechanical property prediction model. This method can improve the accuracy of titanium alloy mechanical property prediction.

Description

Technical Field

[0001] This invention belongs to the field of titanium alloy material research and development, and in particular relates to a method for predicting the mechanical properties of titanium alloys based on active learning. Background Technology

[0002] With the development of titanium alloy material research and development technology, the design space for the combination of composition and process parameters has expanded dramatically. Traditional mechanical property prediction methods mostly rely on empirical formulas or calculation simulations based on density functional theory. These methods are somewhat instructive in simple systems, but they are difficult to handle complex scenarios with multiple coupled factors.

[0003] In traditional methods, researchers typically use empirical models based on "molybdenum equivalent" or construct machine learning models with small samples to fit the statistical relationship between composition, process, and performance using limited experimental data. They also rely on human experience or extensive sampling to screen candidate material formulations in order to gradually approach the target performance.

[0004] However, traditional methods often neglect the strong physical coupling and nonlinear interaction between features in the high-dimensional coupled space of titanium alloy “composition-process-microstructure-property”, which leads to a large amount of information redundancy in the active learning query strategy, significantly reducing the sample utilization efficiency and model convergence speed, resulting in insufficient accuracy in predicting the mechanical properties of titanium alloys. Summary of the Invention

[0005] Therefore, it is necessary to provide a method for predicting the mechanical properties of titanium alloys based on active learning, which can improve the prediction accuracy of the mechanical properties of titanium alloys, in order to address the above-mentioned technical problems.

[0006] Firstly, this application provides a method for predicting the mechanical properties of titanium alloys based on active learning, including:

[0007] Obtain the historical sample vector set. Each historical sample vector in the historical sample vector set includes historical composition process parameter components and labeled mechanical property components.

[0008] Based on historical sample vector sets, the physical relationships characterized by historical component process parameters are analyzed to obtain physical relationship data; among which, the physical relationship data includes physical coupling matrix and parameter causal relationship diagram;

[0009] A physical manifold encoder is constructed based on a set of historical sample vectors;

[0010] A Gaussian process regression model is initialized to obtain an initial prediction model. Based on a preset candidate sample vector set, physical relation data, and physical manifold encoder, the initial prediction model is trained to obtain a trained prediction model for the mechanical properties of titanium alloys. The prediction model for the mechanical properties of titanium alloys is used to predict the mechanical properties of titanium alloys.

[0011] Furthermore, the historical composition process parameter components include at least one process parameter and at least one composition parameter, and the labeled mechanical property components include at least one mechanical property parameter. Based on the historical sample vector set, the physical relationships characterized by the historical composition process parameter components are analyzed to obtain physical relationship data, including:

[0012] Traverse each process parameter and component parameter in the historical sample vector set to form a synthetic parameter pair. For each synthetic parameter pair, use the synthetic parameter pair as the independent variable and any mechanical property parameter in the labeled mechanical property component as the dependent variable to fit a local quadratic surface model of the synthetic parameter pair.

[0013] For each pair of synthetic parameters, the local quadratic surface model is solved to obtain the coupling strength value between the synthetic parameter pair and the mechanical property parameters;

[0014] For each pair of synthesis parameters, the average coupling strength between the synthesis parameter and each mechanical property parameter is calculated to obtain the average coupling strength value of the synthesis parameter pair; and the average coupling strength values ​​of each pair of synthesis parameters are integrated to obtain the physical coupling matrix.

[0015] Using each process parameter and each component parameter as a graph node, an initial parameter relationship graph is obtained;

[0016] Based on the historical sample vector set, the relationships between graph nodes in each initial parameter relationship graph are solved to obtain the parameter causal relationship matrix. Based on the parameter causal relationship matrix, the connection edges between each graph node in the initial parameter relationship graph are constructed to obtain the parameter causal relationship graph.

[0017] Physical relationship data is constructed based on the physical coupling matrix and the parameter causal relationship graph.

[0018] Furthermore, based on the historical sample vector set, the relationships between nodes in the graph of each initial parameter relationship are solved to obtain the parameter causal relationship matrix, including:

[0019] The number of nodes in the initial parameter relationship graph is counted to obtain the total number of nodes, and an initial adjacency matrix is ​​constructed based on the total number of nodes.

[0020] Based on the historical component process parameter elements in the historical sample vector set, a historical parameter matrix is ​​constructed, and the optimized value of the initial adjacency matrix is ​​calculated based on the historical parameter matrix. The expression for the optimized value is:

[0021]

[0022] in, It is the initial adjacency matrix. It is the optimized value of the initial adjacency matrix. It is the number of historical component process parameter components in the historical sample vector set. It is a historical parameter matrix. It is the regularization coefficient;

[0023] Constrained by a preset set of parameter relationship rules, the initial adjacency matrix is ​​adjusted in the direction of reducing the optimization value until the optimization value converges to the minimum value. The initial adjacency matrix corresponding to the minimum optimization value is then used as the parameter causal relationship matrix.

[0024] Furthermore, a physical manifold encoder is constructed based on the historical sample vector set, including:

[0025] Based on the encoder and decoder, an initial variational autoencoder is constructed; and the historical component process parameter components in the historical sample vector set are input into the initial variational autoencoder to obtain the latent variable mean vector, latent variable variance vector and reconstructed feature vector corresponding to the historical component process parameter components.

[0026] Based on the historical component process parameter components, the latent variable mean vector, latent variable variance vector, and reconstructed feature vector corresponding to the historical component process parameter components, the loss function value is calculated. The expression for the loss function value is:

[0027]

[0028] in, It is the value of the loss function. It is the number of historical component process parameter components in the historical sample vector set. It is an index of any historical component's process parameter. It is the first Each historical component and process parameter component It is the first The reconstructed feature vectors corresponding to the historical component process parameter components. It is the regularization weight coefficient. It is the divergence calculation function. It is the standard normal distribution function. It is the first The vector of latent variable means corresponding to each historical component and process parameter. It is the first The variance vector of latent variables corresponding to each historical component process parameter component;

[0029] The initial variational autoencoder is iteratively trained in the direction of minimizing the loss function value until the preset training termination condition is met, resulting in a trained variational autoencoder. The encoder is then extracted from the variational autoencoder as the physical manifold encoder.

[0030] Furthermore, based on a pre-defined candidate sample vector set, physical relation data, and physical manifold encoder, the initial prediction model is trained to obtain a trained prediction model for the mechanical properties of titanium alloys, including:

[0031] Initialize the model training set, and use the initial prediction model as the initial prediction model for the mechanical properties of titanium alloys. Based on the model training set, physical relation data, physical manifold encoder and initial prediction model, execute steps S1 to S6 until the preset convergence condition is met to obtain the prediction model for the mechanical properties of titanium alloys.

[0032] Steps S1 to S6 are as follows:

[0033] S1, For each candidate sample component process parameter component in the candidate sample vector set, input the candidate sample component process parameter component into the titanium alloy mechanical property prediction model to obtain the performance prediction variance value of the candidate sample component process parameter component;

[0034] S2, for each process parameter component of the candidate sample component in the candidate sample vector set, based on the physical coupling matrix and combined with the gradient value of the performance prediction variance relative to the process parameter component of the candidate sample component, the coupling gain factor of the process parameter component of the candidate sample component is calculated.

[0035] S3, for each process parameter component of the candidate sample component in the candidate sample vector set, quantify the influence of the process parameter component of the candidate sample component on the parameter causal relationship diagram, and obtain the causal information value of the process parameter component of the candidate sample component.

[0036] S4. For each process parameter component of the candidate sample component in the candidate sample vector set, input the process parameter component of the candidate sample component into the physical manifold encoder to obtain the latent encoding vector of the process parameter component of the candidate sample component, and quantify the minimum difference between the latent encoding vector and the latent encoding vector of the process parameter components of other training components in the model training set to obtain the minimum spatial distance of the process parameter components of the candidate sample component.

[0037] S5. Based on the performance prediction variance, coupling gain factor, causal information value and minimum spatial distance, the comprehensive utility value of the process parameter component of the candidate sample component is calculated, and the process parameter component of the candidate sample component with the maximum comprehensive utility value is selected as the process parameter component of the training component.

[0038] S6. Obtain the true performance vector of the process parameter components of the training components, add the process parameter components of the training components, the true performance vector of the process parameter components of the training components, and the latent encoding vector to the model training set to obtain a new model training set; and train the titanium alloy mechanical property prediction model based on the new model training set to obtain the updated titanium alloy mechanical property prediction model.

[0039] Furthermore, the expression for the overall utility value is:

[0040]

[0041] in, It is the index of the process parameter component of any candidate sample. It is the first Each candidate sample component contains process parameter components. It is the first The comprehensive utility value of the process parameter components of each candidate sample. It is the first The performance prediction variance of each candidate sample component's process parameter component. It is the first The coupling gain factor of the process parameter components of each candidate sample. It is the first The causal information value of the process parameter components of each candidate sample. It is the first The minimum spatial distance between the process parameter components of each candidate sample. These are the preset bandwidth parameters. These are the coupling gain weighting coefficients. It is the weighted coefficient of causal information value.

[0042] Secondly, this application also provides a device for predicting the mechanical properties of titanium alloys based on active learning, comprising:

[0043] The data acquisition module is used to acquire historical sample vector sets. Each historical sample vector in the historical sample vector set includes historical composition process parameter components and labeled mechanical property components.

[0044] The physical relationship calculation module is used to analyze the physical relationships characterized by historical component process parameters based on historical sample vector sets, and obtain physical relationship data; among which, the physical relationship data includes physical coupling matrix and parameter causal relationship graph;

[0045] The autoencoder building module is used to build a physical manifold encoder based on a set of historical sample vectors.

[0046] The model training module is used to initialize the Gaussian process regression model to obtain the initial prediction model, and to train the initial prediction model based on the preset candidate sample vector set, physical relationship data and physical manifold encoder to obtain the trained titanium alloy mechanical property prediction model; the titanium alloy mechanical property prediction model is used to predict the mechanical properties of titanium alloys.

[0047] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement any of the active learning-based methods for predicting the mechanical properties of titanium alloys described in the first aspect of this application.

[0048] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the active learning-based methods for predicting the mechanical properties of titanium alloys described in the first aspect of this application.

[0049] The aforementioned active learning-based method for predicting the mechanical properties of titanium alloys involves acquiring a historical sample vector set. Each historical sample vector in the set includes historical composition and process parameter components, as well as labeled mechanical property components. Based on this set, the physical relationships represented by the historical composition and process parameter components are analyzed to obtain physical relationship data. This data includes a physical coupling matrix and a parameter causal relationship graph. A physical manifold encoder is constructed based on the historical sample vector set. A Gaussian process regression model is initialized to obtain an initial prediction model. This initial prediction model is then trained using a pre-defined candidate sample vector set, physical relationship data, and the physical manifold encoder to obtain a trained titanium alloy mechanical property prediction model. This model is used to predict the mechanical properties of titanium alloys. This method effectively addresses the problem of information redundancy in high-dimensional, strongly coupled spaces caused by traditional active learning query strategies, improving sample utilization efficiency and model convergence speed, ultimately enhancing the prediction accuracy of titanium alloy mechanical properties. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 A flowchart illustrating a method for predicting the mechanical properties of titanium alloys based on active learning, provided as an embodiment of this application;

[0052] Figure 2 A schematic diagram of a titanium alloy mechanical property prediction device based on active learning, provided as an embodiment of this application;

[0053] Figure 3 This is a schematic diagram of a computer device for predicting the mechanical properties of titanium alloys based on active learning, provided in one embodiment of this application. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0055] In one embodiment, such as Figure 1 As shown, a method for predicting the mechanical properties of titanium alloys based on active learning is provided. This embodiment illustrates the application of this method to a prediction terminal. It is understood that this method can also be applied to a server, and further to a system including both a prediction terminal and a server, and is implemented through the interaction between the prediction terminal and the server. In this embodiment, the method includes the following steps S101-S104, wherein:

[0056] S101, Obtain the historical sample vector set. Each historical sample vector in the historical sample vector set includes historical composition process parameter components and labeled mechanical property components.

[0057] Specifically, the prediction terminal acquires a historical sample vector set. Each historical sample vector in the set includes historical composition and process parameter components and labeled mechanical property components. This historical sample vector set can be obtained from existing titanium alloy experimental databases, publicly published literature data, or internal enterprise historical test records. The format of the historical sample vector set can be... ,in It is a set of historical sample vectors. It is the total number of historical sample vectors in the historical sample vector set. It is the index of the historical sample vector. It is the first A historical sample vector, It is the first The historical component of the process parameter in each historical sample vector It is the first Annotated mechanical property components in a historical sample vector. Historical composition and process parameter components. It can be a multi-dimensional vector used to characterize the composition and processing conditions of a titanium alloy sample. This represents the total number of characteristic dimensions, each corresponding to a factor influencing mechanical properties (such as alloy element content or processing parameters). All dimensions have been standardized (i.e., the mean is subtracted and the value is divided by the standard deviation to eliminate dimensional influence). Any dimension... Annotated mechanical property components of historical sample vectors It can be a A dimensional vector, in the form of ,Include Mechanical property parameters can include tensile strength, yield strength, elongation, and reduction of area. The labeled mechanical property components are data obtained from actual experimental tests on titanium alloy samples, and each component corresponds one-to-one with its corresponding composition and process parameter components. For example, if a historical sample has a composition of Ti-6Al-4V (6% Al, 4% V) and process parameters of solution temperature 950℃, aging temperature 540℃, and aging time 6h, then its historical composition and process parameter components can be expressed as follows: (The specific values ​​depend on the mean and standard deviation of the original data), and the corresponding labeled mechanical property components can be... (Units are MPa, MPa, and %). All historical sample vectors together constitute the historical sample vector set.

[0058] S102, based on the historical sample vector set, analyze the physical relationships of the components of the historical process parameters to obtain physical relationship data; among which, the physical relationship data includes physical coupling matrix and parameter causal relationship diagram.

[0059] Specifically, the prediction terminal uses historical component process parameter components from the historical sample vector set. To analyze the object, the inherent relationships between various feature dimensions are extracted to obtain physical relationship data. This physical relationship data includes a physical coupling matrix and a parameter causal relationship graph. The physical coupling matrix is ​​a symmetric matrix, which can be denoted as... , its first Line number Column elements The historical composition process parameter components were quantified. The feature dimension and the first The local coupling strength between feature dimensions, i.e., the degree of synergy between one feature and another in the impact on performance analysis, is represented by the diagonal elements. The parameter causal relationship graph is a directed acyclic graph, which can be denoted as... , where the node set The number of nodes in the graph is equal to the feature dimension of the historical component process parameter, where each graph node represents a unique feature dimension. (Directed edge set) Each directed edge in Characterizing the features of historical composition process parameters Features There is a direct causal relationship (e.g., solution temperature affects...). There is a physical causal relationship between the phase volume fraction.

[0060] S103, a physical manifold encoder is constructed based on a set of historical sample vectors.

[0061] Specifically, the prediction terminal utilizes historical sample vector sets. Historical component process parameters in Construct a physical manifold encoder. A physical manifold encoder is a nonlinear mapping function. ,in It is the dimension of the low-dimensional physical manifold space, and (For example , Or 4). A physical manifold encoder is used to map historical component process parameters to a preset dimension, so that within this low-dimensional space, the Euclidean distance between two samples can effectively reflect their similarity in the real physical mechanism—that is, samples with similar physical behaviors (such as similar phase transition paths or reinforcement mechanisms) have latent encoded vectors that are close to each other in the manifold space; conversely, samples with large differences in physical mechanisms are far apart. The physical manifold encoder can automatically discover and encode these implicit physical similarity structures from the historical sample vector set through unsupervised learning, and its output can be in the form of… ,in It is called the latent coding vector.

[0062] S104. Initialize the Gaussian process regression model to obtain the initial prediction model. Based on the preset candidate sample vector set, physical relationship data and physical manifold encoder, train the initial prediction model to obtain the trained titanium alloy mechanical property prediction model. The titanium alloy mechanical property prediction model is used to predict the mechanical properties of titanium alloys.

[0063] Specifically, the pre-defined candidate sample vector set This includes a large number of unverified component and process parameter vectors, which can be generated within a predefined design space through Latin hypercube sampling or grid sampling. The feature dimensions of the component and process parameter vectors are consistent with the components of historical component and process parameters, and the values ​​of each feature dimension have been standardized. The prediction terminal uses historical sample vector sets. Based on this, a multi-output Gaussian process regression model is initialized as the initial prediction model. Gaussian process regression is a non-parametric probabilistic model that measures the similarity between input samples by defining a kernel function (such as the autocorrelation determination kernel or the ARD kernel). The initial prediction model can output the mean performance prediction (i.e., the predicted mechanical performance value) and the performance prediction variance (i.e., the prediction uncertainty) corresponding to the input component process vector. During initialization, the prediction terminal optimizes the hyperparameters of the kernel function (such as signal variance, length scale of each feature dimension, and noise variance) by maximizing the log marginal likelihood, and calculates the Cholesky decomposition of the kernel matrix of the training set to obtain the initial prediction model. Then, the initial prediction model enters the active learning training phase: the prediction terminal is based on a preset candidate sample vector set. The initial prediction model is iteratively trained using physical relation data and a variational autoencoder. In each iteration, the prediction terminal uses the current model, physical relation data, and variational autoencoder to select the sample with the most information and lowest redundancy from the candidate set as a recommendation. Its mechanical properties are obtained through real experiments or high-fidelity simulations. This sample is then added to the training set, and the Gaussian process model is updated. This process is repeated until a preset convergence condition is met (e.g., the model performance no longer significantly improves or the maximum number of iterations is reached), ultimately yielding a trained titanium alloy mechanical property prediction model. This titanium alloy mechanical property prediction model can accept any new input vector of composition and process parameters, quickly outputting the corresponding predicted mechanical properties and their confidence intervals, thereby guiding the composition design and process optimization of titanium alloys.

[0064] This embodiment provides a method for predicting the mechanical properties of titanium alloys based on active learning. By acquiring a historical sample vector set, it extracts a physical coupling matrix and a parametric causal relationship graph to quantify the coupling strength and causal structure between features. Simultaneously, it trains a variational autoencoder to learn a low-dimensional physical manifold space. Then, it initializes a Gaussian process regression model and uses the physical relationship data and the variational autoencoder to guide iterative training of active learning. This allows the model to comprehensively consider prediction uncertainty, physical coupling gain, causal information value, and diversity penalty when actively selecting samples in each round, thereby obtaining a high-precision model for predicting the mechanical properties of titanium alloys with the fewest number of experiments. This effectively solves the problem of information redundancy easily generated by traditional active learning query strategies in high-dimensional, strongly coupled spaces, improves sample utilization efficiency and model convergence speed, and ultimately enhances the prediction accuracy of titanium alloy mechanical properties.

[0065] In one embodiment, the historical composition process parameter components include at least one process parameter and at least one composition parameter, and the labeled mechanical property components include at least one mechanical property parameter. Based on the historical sample vector set, the physical relationships represented by the historical composition process parameter components are analyzed to obtain physical relationship data, including:

[0066] S201, traverse each process parameter and component parameter in the historical sample vector set to form a synthetic parameter pair, and for each synthetic parameter pair, use the synthetic parameter pair as the independent variable and any mechanical property parameter in the labeled mechanical property component as the dependent variable to fit the local quadratic surface model of the synthetic parameter pair.

[0067] Specifically, the historical component process parameter component in any historical sample vector Includes at least one process parameter and at least one component parameter Any one of the process parameters The titanium alloy used to characterize this historical sample The content of a certain element (such as aluminum content, vanadium content), any component parameter The titanium alloy used to characterize this historical sample The parameters of the manufacturing process (such as solution temperature, aging time, cooling rate), and historical composition parameters. The form can be And satisfy The prediction terminal is derived from the historical sample vector set. Extract all historical component process parameters and labeled mechanical property components And iterate through all possible combinations of two parameters in all historical sample vectors, that is, from Choose any two different parameters from the parameters. and ( and The combinations include combinations of process parameters and component parameters, combinations of component parameters with component parameters, and combinations of process parameters with process parameters), forming synthesis parameters. For each pair of synthesized parameters, the prediction terminal further iterates through each mechanical property parameter. ( ), with the values ​​of this synthesis parameter pair across all historical sample vectors. As the independent variable, the corresponding mechanical performance parameter value As the dependent variable, a local quadratic surface model is fitted. This model can take the form of: ,in For constant terms, The coefficient of the linear term, The cross term coefficient, The coefficient of the quadratic term.

[0068] S202, for each pair of synthetic parameters, solve the local quadratic surface model to obtain the coupling strength value between the synthetic parameter pair and the mechanical performance parameters.

[0069] Specifically, for each pair of synthesis parameters and each mechanical performance parameter The prediction terminal uses the least squares method to solve the local quadratic surface model, that is, to find the set of coefficients that minimizes the sum of squared errors between the model's predicted values ​​and the actual values ​​at all sample points, and then extracts the cross-term coefficients from it. The absolute value of the cross term coefficient reflects the parameter and In common influence performance parameters The strength of the nonlinear interaction at time: The larger the absolute value, the more significant the coupling effect between the two parameters, that is, the stronger the synergistic or antagonistic effect on performance when the two parameters change together. The prediction terminal defines the absolute value of the cross-term coefficient as the coupling strength of the combined parameter pair under the current mechanical performance parameters, denoted as . The prediction terminal repeats the above operation of extracting absolute values ​​for each pair of synthetic parameters and each mechanical property parameter to obtain the coupling strength value of all pairs of synthetic parameters and each mechanical property parameter.

[0070] S203, for each pair of synthetic parameters, the average coupling strength between the synthetic parameter and each mechanical property parameter is calculated to obtain the average coupling strength value of the synthetic parameter pair; and the average coupling strength values ​​of each pair of synthetic parameters are integrated to obtain the physical coupling matrix.

[0071] Specifically, for each pair of synthesis parameters The prediction terminal has already obtained its all Coupling strength value under mechanical performance parameters Then, the predicted terminal takes the arithmetic mean of these values ​​to obtain the composite parameter pair. Average coupling strength value: This average value reflects the parameter and The average coupling degree across the entire mechanical performance space. Predicting terminal initialization. zero matrix ( (This refers to the dimension of historical composition and process parameter components), and then iterates through all synthesis parameter pairs. , calculate Fill the first part of the matrix Line number Column, at the same time Assign to Also set diagonal elements Keeping it as 0, the final matrix is This is the physical coupling matrix, which fully records the average coupling strength between all component parameters and process parameters, between component parameters and process parameters, and serves as prior knowledge for subsequent active learning.

[0072] S204. Using each process parameter and each component parameter as a graph node, an initial parameter relationship graph is obtained.

[0073] Specifically, the prediction terminal will use historical component process parameters. Each dimension (i.e., each process parameter and each component parameter) is considered a node in a directed graph. Let there be a total of... Each node corresponds to Each node has a feature (e.g., node 1 represents aluminum content, node 2 represents vanadium content, node 3 represents solution temperature, etc.). The prediction terminal creates an empty graph structure. , where the node set The edge set is initially empty. This initial parametric graph does not yet contain any connecting edges; it only determines the number and identifiers of the nodes.

[0074] S205. Based on the historical sample vector set, solve the relationship between the graph nodes in each initial parameter relationship graph to obtain the parameter causal relationship matrix. Based on the parameter causal relationship matrix, construct the connection edges between each graph node in the initial parameter relationship graph to obtain the parameter causal relationship graph.

[0075] Specifically, the prediction terminal uses historical sample vector sets Historical component process parameters in As a data sample, the initial parameter relationship diagram Based on the node set, the directed dependencies between nodes are solved using a causal discovery algorithm to obtain the parametric causal relationship matrix. Parameter causal relationship matrix Central African zero element This indicates the existence of nodes in the graph. Pointing to graph nodes The directed edges, i.e., the parameters It is a parameter The direct cause is zero; zero elements indicate the absence of a direct causal relationship. This is used to obtain the parameter causal relationship matrix. Then, the prediction terminal uses the parameter causality matrix. For non-zero elements in the initial parameter relationship graph, a directed edge is added to the corresponding node pair: if Then add a node from the graph. To graph nodes Directed edges. All directed edges form the edge set. Thus, a complete parameter causal relationship diagram is obtained. At the same time, for each non-zero element in the matrix ,if The absolute value is less than the preset confidence threshold (e.g.) The prediction terminal will add the connection edge to the set of undetermined edges. This indicates that the current data is insufficient to reliably determine the causal direction; conversely, if If the absolute value is greater than or equal to the preset confidence threshold, the direction is considered determined. The prediction terminal will also traverse all graph node pairs in the parameter causal relationship graph. Identify nodes from the cause graph To the result graph node A non-causal path between nodes, which contains a node that simultaneously affects the graph. Graph Nodes Hybrid graph nodes (For example, If there exists a node in the graph To graph nodes If a path other than the directed path (i.e., not along the edge direction and containing a branching structure) is found, then the graph node pair is added to the backdoor path node pair set. The set of backdoor path node pairs can be used in active learning to evaluate whether candidate samples help to block confounding bias, thereby improving the accuracy of causal inference.

[0076] S206, based on the physical coupling matrix and parameter causal relationship graph, constitutes physical relationship data.

[0077] Specifically, the prediction terminal will use the physical coupling matrix Parameter causal relationship diagram And the set of undetermined edges obtained in S205 and backdoor path node pair set By combining the data, we can obtain complete physical relationship data.

[0078] This embodiment provides a method for predicting the mechanical properties of titanium alloys based on active learning. It iterates through all compositional and process parameters to form synthetic parameter pairs. For each synthetic parameter pair, a local quadratic surface model is fitted, and the absolute values ​​of the cross-term coefficients are extracted. Then, the average of all mechanical properties is calculated to construct a physical coupling matrix that quantifies the coupling strength between features. Simultaneously, using each parameter as a graph node, causal relationships are solved based on historical sample vector sets to obtain a parameter causal relationship matrix and construct directed edges, forming a parameter causal relationship graph containing undetermined edges and backdoor path information. Finally, the physical coupling matrix and the parameter causal relationship graph are combined to form physical relationship data. This explicitly encodes the nonlinear interactions and causal structures in titanium alloy metallurgy as prior knowledge, providing physical information enhancement utility evaluation data for subsequent active learning query strategies. This effectively reduces redundant sampling, accelerates model convergence, and thus improves the accuracy and efficiency of mechanical property prediction.

[0079] In one embodiment, based on a historical sample vector set, the relationships between nodes in the initial parameter relationship graph are solved to obtain a parameter causal relationship matrix, including:

[0080] S301, count the number of nodes in the initial parameter relationship graph to obtain the total number of nodes, and construct the initial adjacency matrix based on the total number of nodes.

[0081] Specifically, the prediction terminal is based on the initial parameter relationship graph. The number of graph nodes is obtained, where each graph node corresponds to a historical component of the process parameters. One of the feature dimensions (i.e., a component parameter or a process parameter), and The total number of all graph nodes is Predicting the terminal initializes a square array This is called the initial adjacency matrix. Each row and column of this matrix corresponds to the same set of nodes, where the nth row is the first row and the second column is the second row and the third column. Line number Column elements Indicates whether there exists a node in the graph. Pointing to graph nodes Directed edges (i.e., parameters) Is it a parameter? (The direct cause). During initialization, it can be... All elements are set to small random values ​​(e.g., following a normal distribution with a mean of 0 and a variance of 0.01), or all are set to zero.

[0082] S302, based on the historical component process parameter elements in the historical sample vector set, construct a historical parameter matrix, and calculate the optimized value of the initial adjacency matrix based on the historical parameter matrix. The expression for the optimized value is:

[0083]

[0084] in, It is the initial adjacency matrix. It is the optimized value of the initial adjacency matrix. It is the number of historical component process parameter components in the historical sample vector set. It is a historical parameter matrix. It is the regularization coefficient.

[0085] Specifically, the prediction terminal uses historical sample vector sets. Historical component process parameters in To calculate the optimized value of the initial adjacency matrix. First, all... indivual Stacked row by row to form a historical parameter matrix Each row represents a historical sample vector containing historical component process parameters. Optimized values It consists of two parts: Part 1 It is the reconstruction error term, where This represents the Frobenius norm (the square root of the sum of the squares of all elements of a matrix). This term measures the value of the initial adjacency matrix. For the historical parameter matrix Perform linear transformation Later compared with the original history parameter matrix The difference between them, in its physical sense, is: if there exists a node from the graph... To graph nodes If there are causal edges, then the values ​​of other nodes can be used to linearly predict the graph nodes. The smaller the reconstruction error, the better the initial adjacency matrix. The higher the fit to the linear causal relationship in the data, the better. Part Two It is a sparse regularization term, in which It represents the L1 norm (i.e., the sum of the absolute values ​​of all elements of a matrix). This is a preset regularization coefficient (e.g., 0.01 or 0.1) used to control the sparsity of the initial adjacency matrix. A larger preset regularization coefficient results in fewer non-zero elements in the initial adjacency matrix, thus encouraging a simpler causal structure and avoiding overfitting. The optimized value calculated by the prediction terminal is a scalar value whose magnitude reflects the balance between fitting the data and maintaining sparsity in the initial adjacency matrix.

[0086] S303, constrained by a preset set of parameter relationship rules, adjusts the initial adjacency matrix in the direction of reducing the optimization value until the optimization value converges to the minimum value, and uses the initial adjacency matrix corresponding to the minimum optimization value as the parameter causal relationship matrix.

[0087] Specifically, the pre-defined set of parameter relationship rules is a set of rules predefined based on knowledge in the field of titanium alloy metallurgy. It includes two types of mandatory constraints: a set of mandatory causal rules and a set of mandatory non-causal rules. The set of mandatory causal rules is used to characterize the causal relationship between any parameters as known and certain (e.g., "aluminum content → α phase volume fraction"), and is used to instruct the corresponding elements in the initial adjacency matrix to maintain non-zero values ​​during the optimization process (which can be set to be greater than a certain small positive number). (e.g., 0.1); the forced non-causal rule set is used to characterize that the causal relationship between any parameters does not exist, and is used to indicate that the corresponding elements in the initial adjacency matrix remain at zero during the optimization process. The preset parameter relationship rule set can be set according to the characteristic dimensions and actual laws of historical component process parameters in actual work. The prediction terminal uses a preset parameter relationship rule set as a prior constraint to iteratively optimize the initial adjacency matrix. Specifically, gradient descent or its variants (such as the Adam optimizer) can be used to repeatedly adjust the initial adjacency matrix. In each iteration, the gradient of the optimized value with respect to the initial adjacency matrix is ​​calculated first, and then the elements in the initial adjacency matrix are updated along the gradient descent direction, thereby reducing the optimized value. After each update, the prediction terminal adjusts the values ​​of the corresponding elements in the updated initial adjacency matrix with the preset parameter relationship rule set. The above iterative process is repeated until the change in the optimized value is less than a preset threshold (e.g., 0.1). If the maximum number of iterations is reached (e.g., 10,000), the optimized value is considered to have converged to the minimum value. The prediction terminal uses the currently updated initial adjacency matrix as the parameter causality matrix. The non-zero elements in the parameter causality matrix indicate the directed causal relationship between the parameters.

[0088] This embodiment provides a method for predicting the mechanical properties of titanium alloys based on active learning. An initial adjacency matrix is ​​constructed using the number of nodes in a statistical graph. An optimization objective function incorporating reconstruction error and sparse regularization is defined. A pre-defined set of parameter relationship rules is used as a hard constraint to iteratively adjust the adjacency matrix until convergence, ultimately yielding a parameter causal relationship matrix. Prior causal knowledge from titanium alloy metallurgy is explicitly integrated into the causal discovery process, avoiding spurious causal relationships that may arise from purely data-driven methods. Simultaneously, sparse regularization ensures the simplicity of the causal graph, resulting in a more reliable and interpretable causal structure between parameters. This provides a solid foundation for evaluating the value of causal information in subsequent active learning.

[0089] In one embodiment, a physical manifold encoder is constructed based on a set of historical sample vectors, including:

[0090] S401, based on the encoder and decoder, constructs an initial variational autoencoder; and inputs the historical component process parameter components from the historical sample vector set into the initial variational autoencoder to obtain the latent variable mean vector, latent variable variance vector, and reconstructed feature vector corresponding to the historical component process parameter components.

[0091] Specifically, the prediction terminal constructs an initial variational autoencoder, which is obtained by concatenating two neural network modules: an encoder and a decoder. The encoder... Used to receive historical composition and process parameter components It is then mapped to a low-dimensional space, and the latent coded sample values ​​are output. It is assumed that the posterior distribution of the initial variational autoencoder follows a diagonal Gaussian distribution, and the encoder outputs the latent variable mean vector. and the log-variance vector of latent variables Two vectors, where the logarithmic variance vector of the latent variable is used to perform an exponential operation to obtain the variance vector of the latent variable. Decoder The latent encoded sample values ​​output by the encoder are then mapped back to the original data space, and the output is a reconstructed feature vector with the same dimension as the input historical component process parameter components. The prediction terminal will use historical sample vector sets. All historical component process parameters The data is sequentially input into the initial variational autoencoder. For each historical component process parameter... The encoder calculates the corresponding latent variable mean vector. and latent variable variance vector Then, the latent coding sample value is obtained by using the reparameterization technique. ,in It is standard normal noise. This represents element-wise multiplication. Finally, Input to the decoder to obtain the reconstructed feature vector. For example, suppose , For the first historical component process parameter component Encoder output , ,but After reparameterization, we get Decoder output .

[0092] S402, based on the historical composition process parameter components, the latent variable mean vector, latent variable variance vector corresponding to the historical composition process parameter components, and the reconstructed feature vector, the loss function value is calculated. The expression for the loss function value is:

[0093]

[0094] in, It is the value of the loss function. It is the number of historical component process parameter components in the historical sample vector set. It is an index of any historical component's process parameter. It is the first Each historical component and process parameter component It is the first The reconstructed feature vectors corresponding to the historical component process parameter components. It is the regularization weight coefficient. It is the divergence calculation function. It is the standard normal distribution function. It is the first The vector of latent variable means corresponding to each historical component and process parameter. It is the first The variance vector of latent variables corresponding to each historical component process parameter.

[0095] Specifically, the prediction terminal uses all historical component process parameter components, the latent variable mean vector, the latent variable variance vector, and the reconstructed feature vector obtained in step S401 to calculate the loss function value of the variational autoencoder. This loss function consists of a weighted sum of two terms: the first term... It is the reconstruction loss, expressed in the form of mean squared error (MSE), where This represents the L2 norm (the square root of the sum of the squares of the elements of the vector). This term measures the reconstructed feature vector generated by the decoder. Corresponding historical component process parameters The smaller the reconstruction loss, the better the variational autoencoder retains the effective information of the input data. (Second term) It is the regularization loss, where the divergence calculation function is... This refers to calculating the Kullback-Leibler divergence, used to measure the distribution of latent variables in the encoder output. Compared with the standard normal distribution The difference between them. The specific formula for calculating the KL divergence is: Preset regularization weight coefficients Used to adjust the strength of the regularization term, for example Alternatively, version 1.0 can be configured according to actual work requirements; The larger the value, the closer the latent variable distribution is to the standard normal distribution, thus obtaining a more regular and continuous latent space.

[0096] S403, in the direction of minimizing the loss function value, iteratively train the initial variational autoencoder until the preset training termination condition is met, and obtain the trained variational autoencoder, and extract the encoder from the variational autoencoder as the physical manifold encoder.

[0097] Specifically, the prediction terminal uses gradient descent-type optimization algorithms (such as the Adam optimizer) to optimize the parameters of the initial variational autoencoder (encoder parameters). and decoder parameters The algorithm iteratively updates the parameters of the encoder. In each iteration, the prediction terminal calculates the loss function and updates the parameters of the encoder. and decoder parameters The gradient is calculated, and then the parameters are adjusted along the gradient descent direction to reduce the loss function value. During training, the prediction terminal monitors the changes in the loss function value until a preset training termination condition is met, resulting in a trained variational autoencoder. The preset training termination condition can be one of the following: the change in the loss function value over several consecutive rounds (e.g., 10 rounds) is less than a preset threshold (e.g., ...). The iteration count can be set to either 5000 or a preset maximum number of iterations. The resulting variational autoencoder's encoder portion has stabilized and will map high-dimensional historical component process parameter components to a low-dimensional physical manifold space. The prediction terminal extracts the encoder module (i.e., encoder parameters) from the trained variational autoencoder. (and its corresponding network structure), which is used as a physical manifold encoder. The physical manifold encoder receives arbitrary standardized component process parameter vectors. Vector of composition and process parameters The latent variable mean vector is output as the latent coding vector, i.e., the latent coding vector. This compresses the original high-dimensional input into a low-dimensional manifold space, which is then used for diversity evaluation in subsequent active learning.

[0098] This embodiment provides a method for predicting the mechanical properties of titanium alloys based on active learning. It constructs an initial variational autoencoder consisting of an encoder and a decoder, inputting historical composition and process parameter components into the model to obtain the latent variable mean, variance, and reconstruction vector. A loss function, weighted by the reconstruction loss and a KL divergence regularization term, is calculated and iteratively minimized until convergence. Finally, the encoder is extracted from the trained variational autoencoder as the physical manifold encoder. By utilizing the variational autoencoder to unsupervisedly learn the low-dimensional nonlinear manifold structure of titanium alloy composition and process parameters, samples that are close in the manifold space have similar physical mechanisms. This provides a quantitative basis for the diversity penalty factor in active learning based on physical similarity, avoiding the failure problem of traditional Euclidean distance in high-dimensional sparse spaces and improving the accuracy and representativeness of model training sample selection.

[0099] In one embodiment, an initial prediction model is trained based on a preset candidate sample vector set, physical relationship data, and a physical manifold encoder to obtain a trained prediction model for the mechanical properties of titanium alloys, including:

[0100] S501, initialize the model training set, and use the initial prediction model as the initial prediction model for the mechanical properties of titanium alloys. Based on the model training set, physical relationship data, physical manifold encoder and initial prediction model, execute steps S1 to S6 until the preset convergence condition is met, and obtain the prediction model for the mechanical properties of titanium alloys.

[0101] Specifically, the prediction terminal first initializes the model training set, which includes the historical sample vector set. As the initial model training set, To train the component process parameters, an initial prediction model for the mechanical properties of titanium alloys is created using the initial prediction model. Then, the prediction terminal enters an active learning loop, repeatedly executing steps S1 to S6. In each round, a new, experimentally validated sample is added to the model training set, and the model is updated. This loop continues until a preset convergence condition is met. The preset convergence condition can be that the rate of change of the prediction error of the titanium alloy mechanical property prediction model on the model training set in the most recent several rounds (e.g., 10 rounds) is less than a threshold (e.g., ...). The convergence condition can be set if: the overall utility value of the samples selected in the current round is lower than a preset threshold (e.g., 0.01); or the number of iterations performed has reached the maximum budget (e.g., 50). The preset convergence condition can be set according to the actual work.

[0102] Steps S1 to S6 are as follows:

[0103] S1, for each candidate sample component process parameter component in the candidate sample vector set, input the candidate sample component process parameter component into the titanium alloy mechanical property prediction model to obtain the performance prediction variance value of the candidate sample component process parameter component.

[0104] Specifically, the prediction terminal will use a pre-set set of candidate sample vectors. Each candidate sample component process parameter component The input is fed into the current titanium alloy mechanical property prediction model, which calculates the performance prediction variance of the candidate sample composition and process parameter components. Performance prediction variance The uncertainty of the current titanium alloy mechanical property prediction model in predicting the process parameter components of candidate sample composition was quantified. The larger the performance prediction variance value, the more uncertain the current titanium alloy mechanical property prediction model is in predicting the process parameter components of the candidate sample composition. Therefore, the process parameter components of the candidate sample composition have more exploratory value.

[0105] S2, for each process parameter component of the candidate sample component in the candidate sample vector set, based on the physical coupling matrix and combined with the gradient value of the performance prediction variance relative to the process parameter component of the candidate sample component, the coupling gain factor of the process parameter component of the candidate sample component is calculated.

[0106] Specifically, for each candidate sample component's process parameter component, the prediction terminal first calculates the performance prediction variance. The first-order partial derivatives of each feature dimension component in the process parameter component of the candidate sample ( This partial derivative can be solved analytically: ,and ,in It is the kernel function in the initial prediction model for the first... A vector of partial derivatives of the input. After obtaining all partial derivatives, the prediction terminal is combined with the physical coupling matrix. The coupling gain factor of the process parameter components of the candidate sample was calculated. The coupling gain factor reflects the coupling strength of parameters in each dimension within the process parameter component of the candidate sample.

[0107] S3. For each process parameter component of the candidate sample in the candidate sample vector set, quantify the influence of the process parameter component of the candidate sample on the parameter causal relationship diagram, and obtain the causal information value of the process parameter component of the candidate sample.

[0108] Specifically, for each candidate sample component's process parameter component, the prediction terminal utilizes the parameter causal relationship graph in the physical relationship data. Undetermined set of edges and backdoor path node pair set This involves quantifying the impact of process parameter components of candidate sample components on the parameter causal relationship graph. Specifically, it evaluates whether these process parameter components can help determine the causal direction of a connection edge in the undetermined edge set, or help block backdoor paths between a pair of graph nodes in the backdoor path node pair set. For each connection edge in the undetermined edge set... (in and (These are two different graph nodes, corresponding to two feature dimensions), the prediction terminal calculates the process parameter components of the candidate sample in the feature dimension. and The minimum Euclidean distance between the value of the process parameter component on the same feature and the values ​​of all training components in the current model training set on the same feature: ,in This refers to the number of process parameter components in the current model training set. The prediction terminal predicts based on a preset distance threshold. ,like Then it is considered that the process parameter components of the candidate sample are... When a combination of values ​​falls into an area not covered by existing data, conducting experiments at that point can provide new information to help determine the connection edges. The causal direction, and the directional contribution value at this time. Add 1 (initial) (0). Secondly, for each pair of graph nodes in the backdoor path node pair set. The prediction terminal identifies the mixed graph nodes from which the graph node pair is extracted. To form a set of mixed variables For each node in the hybrid graph The prediction terminal calculates the component process parameter components of candidate samples in the feature The values ​​on the feature are related to the process parameter components of all training components in the current model training set. The minimum absolute difference between the values ​​of: .like Greater than the preset impact threshold If so, then the process parameter component of the candidate sample is considered to be in the confounding variables. The above provides new value combinations that help block the backdoor path (i.e., distinguish between confounding factors and causal effects), at which point the backdoor contribution value... Add 1 (initial) (0). Predicting the terminal for the undetermined set of edges. After traversing all elements in the set of backdoor path nodes, the accumulated directional contribution value will be... and backdoor contribution value By adding them together, we obtain the causal information value of the process parameter components of the candidate sample. The value of causal information The larger the value, the more helpful the process parameter component of the candidate sample is in revealing or confirming a causal relationship.

[0109] S4. For each process parameter component of the candidate sample component in the candidate sample vector set, input the process parameter component of the candidate sample component into the physical manifold encoder to obtain the latent encoding vector of the process parameter component of the candidate sample component, and quantify the minimum difference between the latent encoding vector and the latent encoding vector of the process parameter components of other training components in the model training set to obtain the minimum spatial distance of the process parameter components of the candidate sample component.

[0110] Specifically, for each candidate sample component's process parameter component, the prediction terminal inputs the candidate point's candidate sample component's process parameter component into the physical manifold encoder. The physical manifold encoder outputs the latent variable mean vector of that candidate point as the latent encoding vector. (The dimension is the low-dimensional manifold space). Simultaneously, the prediction terminal inputs the process parameter components of each training component in the current model training set into the physical manifold encoder to obtain their latent encoded vectors. Then, the prediction terminal calculates the Euclidean distance between the latent encoded vectors of the process parameter components of the candidate sample component and the latent encoded vectors of the process parameter components of other training components in the model training set, and takes the minimum value as the minimum spatial distance of the candidate sample component's process parameter component. The minimum spatial distance reflects the distance of the candidate sample component's process parameter component to the closest existing sample in the low-dimensional physical manifold space. The larger the minimum spatial distance, the greater the difference in physical mechanism between the candidate point and the existing samples, and the greater its diversity.

[0111] S5. Based on the performance prediction variance, coupling gain factor, causal information value, and minimum spatial distance, the comprehensive utility value of the process parameter component of the candidate sample component is calculated, and the process parameter component of the candidate sample component with the maximum comprehensive utility value is selected as the process parameter component of the training component.

[0112] Specifically, for each candidate sample component's process parameter component, the prediction terminal substitutes its performance prediction variance, coupling gain factor, causal information value, and minimum spatial distance into the comprehensive utility function to calculate the comprehensive utility value. The design principle of the comprehensive utility function is: the higher the prediction uncertainty, the greater the physical coupling gain, the higher the causal information value, and the farther the candidate point is from the manifold distance of existing samples, the greater its comprehensive utility value. After the prediction terminal traverses all candidate sample component process parameter components, it selects the candidate sample component process parameter component with the largest comprehensive utility value and uses it as the training component process parameter component for this round of iteration.

[0113] S6. Obtain the true performance vector of the process parameter components of the training components, add the process parameter components of the training components, the true performance vector of the process parameter components of the training components, and the latent encoding vector to the model training set to obtain a new model training set; and train the titanium alloy mechanical property prediction model based on the new model training set to obtain the updated titanium alloy mechanical property prediction model.

[0114] Specifically, the prediction terminal restores the process parameter components of the training components selected in the current round to their original scale (de-standardization) and submits them to the actual titanium alloy preparation and mechanical property testing. The corresponding real mechanical property vectors are obtained through experiments or high-fidelity simulations. Then, the prediction terminal adds the training component process parameter components, the true performance vectors of the training component process parameter components, and the latent encoding vectors to the model training set, obtaining an updated training set. The prediction terminal then updates the current titanium alloy mechanical property prediction model based on the new training set. Incremental learning methods can be used to improve efficiency during the update, resulting in an updated titanium alloy mechanical property prediction model, which will serve as the current titanium alloy mechanical property prediction model for the next iteration.

[0115] This embodiment provides a method for predicting the mechanical properties of titanium alloys based on active learning. It initializes the model training set and prediction model, then repeatedly executes the following active learning loop: generating a candidate set and calculating the prediction variance for each candidate point; calculating the coupling gain factor based on the physical coupling matrix and the prediction variance gradient; quantifying the causal information value based on the parametric causal relationship graph and its set of undetermined edges and backdoor paths; obtaining the latent encoding vector through a physical manifold encoder and calculating the minimum spatial distance; integrating the above four items into a comprehensive utility value and selecting the sample corresponding to the maximum value as the experimental recommendation; after obtaining the true performance, expanding the training set and incrementally updating the Gaussian process model until the convergence condition is met. By explicitly integrating the physical coupling structure, causal prior knowledge, and low-dimensional manifold similarity into the active learning query strategy, the selected samples in each round possess high uncertainty, high physical information gain, high causal discovery value, and high diversity. This significantly improves the accuracy and generalization ability of the titanium alloy mechanical property prediction model with the fewest number of experiments, effectively reducing the experimental cost and time cycle in materials research and development.

[0116] In one embodiment, the expression for the overall utility value is:

[0117]

[0118] in, It is the index of the process parameter component of any candidate sample. It is the first Each candidate sample component contains process parameter components. It is the first The comprehensive utility value of the process parameter components of each candidate sample. It is the first The performance prediction variance of each candidate sample component's process parameter component. It is the first The coupling gain factor of the process parameter components of each candidate sample. It is the first The causal information value of the process parameter components of each candidate sample. It is the first The minimum spatial distance between the process parameter components of each candidate sample. These are the preset bandwidth parameters. These are the coupling gain weighting coefficients. It is the weighted coefficient of causal information value.

[0119] Specifically, in each iteration of the active learning process, the prediction terminal calculates the comprehensive utility value of each candidate sample component (process parameter component) in the candidate sample vector set using the formula described above. This formula combines four sub-terms with different physical meanings in a product form. Its design aims to simultaneously maximize model prediction uncertainty, physical coupling gain, causal information value, and sample diversity. In the formula, the performance prediction variance... It is calculated based on the Gaussian process regression model in step S1, reflecting the degree of prediction uncertainty of the model at the current candidate sample. Coupling gain factor It is calculated based on the physical coupling matrix and predicted variance gradient in step S2, and is used to characterize the coupling strength of the region where the candidate sample is located. Causal information value. It is obtained by quantizing the set based on the parameter causal relationship graph, its undetermined edge set, and backdoor path nodes in step S3. Minimum spatial distance This is calculated using the physical manifold encoder in step S4, and represents the minimum Euclidean distance between the latent codes of candidate samples and existing training samples. The fourth step in the formula... Yes The nonlinear mapping, where This is a preset bandwidth parameter, which can be set to the median of the pairwise distances between the latent encoded vectors of all training components (process parameter components) in the model training set; when When the value is very small, this factor approaches 0, resulting in a strong penalty to the overall utility value (avoiding the selection of redundant samples that are too similar to existing samples); when... When the value is large, this term approaches 1, and the penalty disappears. Coupling gain weighting coefficient. And causal information value weighting coefficient These are preset weighting coefficients used to adjust the relative importance of the coupling gain factor and the causal information value in the overall utility. For example, they can be set to... , After calculating the combined utility value of all candidate samples, the terminal selects the candidate sample with the highest value as the recommended sample for the experiment.

[0120] This embodiment provides a method for predicting the mechanical properties of titanium alloys based on active learning. By constructing a product-type comprehensive utility function that includes prediction uncertainty, physical coupling gain factor, causal information value, and a diversity penalty factor based on manifold distance, and introducing adjustable weighting coefficients and bandwidth parameters, it achieves multi-dimensional quantification and fusion of candidate sample information. This formula adaptively balances the relationship between exploration (high uncertainty, high coupling, high causal value) and utilization (low diversity penalty), thereby stably selecting the experimental samples with the most comprehensive value during active learning iterations, significantly improving the sample efficiency of model training and the final prediction accuracy.

[0121] In the aforementioned active learning-based method for predicting the mechanical properties of titanium alloys, a historical sample vector set is acquired. Each historical sample vector in the set includes historical composition and process parameter components and labeled mechanical property components. Based on the historical sample vector set, the physical relationships represented by the historical composition and process parameter components are analyzed to obtain physical relationship data. This physical relationship data includes a physical coupling matrix and a parameter causal relationship graph. A physical manifold encoder is constructed based on the historical sample vector set. A Gaussian process regression model is initialized to obtain an initial prediction model. Based on a pre-set candidate sample vector set, physical relationship data, and physical manifold encoder, the initial prediction model is trained to obtain a trained titanium alloy mechanical property prediction model. This model is used to predict the mechanical properties of titanium alloys. This method effectively solves the problem of information redundancy that traditional active learning query strategies easily generate in high-dimensional, strongly coupled spaces, improves sample utilization efficiency and model convergence speed, and ultimately enhances the prediction accuracy of titanium alloy mechanical properties.

[0122] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0123] Based on the same inventive concept, this application also provides an active learning-based titanium alloy mechanical property prediction device for implementing the active learning-based titanium alloy mechanical property prediction method described above. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the active learning-based titanium alloy mechanical property prediction device provided below can be found in the limitations of the active learning-based titanium alloy mechanical property prediction method described above, and will not be repeated here.

[0124] In one exemplary embodiment, such as Figure 2 As shown, a titanium alloy mechanical property prediction device 200 based on active learning is provided, comprising:

[0125] The data acquisition module 201 is used to acquire a historical sample vector set. Each historical sample vector in the historical sample vector set includes historical composition process parameter components and labeled mechanical property components.

[0126] The physical relationship calculation module 202 is used to analyze the physical relationships characterized by historical component process parameters based on historical sample vector sets to obtain physical relationship data; wherein, the physical relationship data includes a physical coupling matrix and a parameter causal relationship graph;

[0127] Autoencoder building module 203 is used to build a physical manifold encoder based on a set of historical sample vectors;

[0128] The model training module 204 is used to initialize the Gaussian process regression model to obtain the initial prediction model, and to train the initial prediction model based on the preset candidate sample vector set, physical relationship data and physical manifold encoder to obtain the trained titanium alloy mechanical property prediction model; the titanium alloy mechanical property prediction model is used to predict the mechanical properties of titanium alloy.

[0129] Furthermore, the historical composition process parameter component includes at least one process parameter and at least one composition parameter, the labeled mechanical property component includes at least one mechanical property parameter, and the physical relationship calculation module may also include:

[0130] The surface model construction unit is used to traverse each process parameter and component parameter in the historical sample vector set, form a synthetic parameter pair, and for each synthetic parameter pair, with the synthetic parameter pair as the independent variable and any mechanical property parameter in the labeled mechanical property component as the dependent variable, fit to obtain the local quadratic surface model of the synthetic parameter pair.

[0131] A single strength calculation unit is used to solve the local quadratic surface model for each pair of synthetic parameters to obtain the coupling strength value between the pair of synthetic parameters and the mechanical property parameters.

[0132] The coupling matrix construction unit is used to calculate the average coupling strength between the synthesis parameter and each mechanical property parameter for each synthesis parameter pair, and to obtain the average coupling strength value of the synthesis parameter pair; and to integrate the average coupling strength values ​​of each synthesis parameter pair to obtain the physical coupling matrix.

[0133] The initial relationship diagram construction unit is used to obtain the initial parameter relationship diagram with each process parameter and each component parameter as a graph node;

[0134] The parameter causal relationship graph construction unit is used to solve the relationship between graph nodes in each initial parameter relationship graph based on the historical sample vector set, obtain the parameter causal relationship matrix, and construct the connection edges between each graph node in the initial parameter relationship graph based on the parameter causal relationship matrix to obtain the parameter causal relationship graph.

[0135] The physical relationship data integration unit is used to assemble physical relationship data based on the physical coupling matrix and the parameter causal relationship graph.

[0136] Furthermore, the parameter causal relationship graph building unit can also be used for:

[0137] The number of nodes in the initial parameter relationship graph is counted to obtain the total number of nodes, and an initial adjacency matrix is ​​constructed based on the total number of nodes.

[0138] Based on the historical component process parameter elements in the historical sample vector set, a historical parameter matrix is ​​constructed, and the optimized value of the initial adjacency matrix is ​​calculated based on the historical parameter matrix. The expression for the optimized value is:

[0139]

[0140] in, It is the initial adjacency matrix. It is the optimized value of the initial adjacency matrix. It is the number of historical component process parameter components in the historical sample vector set. It is a historical parameter matrix. It is the regularization coefficient;

[0141] Constrained by a preset set of parameter relationship rules, the initial adjacency matrix is ​​adjusted in the direction of reducing the optimization value until the optimization value converges to the minimum value. The initial adjacency matrix corresponding to the minimum optimization value is then used as the parameter causal relationship matrix.

[0142] Furthermore, the autoencoder building block can also be used for:

[0143] Based on the encoder and decoder, an initial variational autoencoder is constructed; and the historical component process parameter components in the historical sample vector set are input into the initial variational autoencoder to obtain the latent variable mean vector, latent variable variance vector and reconstructed feature vector corresponding to the historical component process parameter components.

[0144] Based on the historical component process parameter components, the latent variable mean vector, latent variable variance vector, and reconstructed feature vector corresponding to the historical component process parameter components, the loss function value is calculated. The expression for the loss function value is:

[0145]

[0146] in, It is the value of the loss function. It is the number of historical component process parameter components in the historical sample vector set. It is an index of any historical component's process parameter. It is the first Each historical component and process parameter component It is the first The reconstructed feature vectors corresponding to the historical component process parameter components. It is the regularization weight coefficient. It is the divergence calculation function. It is the standard normal distribution function. It is the first The vector of latent variable means corresponding to each historical component and process parameter. It is the first The variance vector of latent variables corresponding to each historical component process parameter component;

[0147] The initial variational autoencoder is iteratively trained in the direction of minimizing the loss function value until the preset training termination condition is met, resulting in a trained variational autoencoder. The encoder is then extracted from the variational autoencoder as the physical manifold encoder.

[0148] Furthermore, the model training module can also be used for:

[0149] Initialize the model training set, and use the initial prediction model as the initial prediction model for the mechanical properties of titanium alloys. Based on the model training set, physical relation data, physical manifold encoder and initial prediction model, execute steps S1 to S6 until the preset convergence condition is met to obtain the prediction model for the mechanical properties of titanium alloys.

[0150] Steps S1 to S6 are as follows:

[0151] S1, For each candidate sample component process parameter component in the candidate sample vector set, input the candidate sample component process parameter component into the titanium alloy mechanical property prediction model to obtain the performance prediction variance value of the candidate sample component process parameter component;

[0152] S2, for each process parameter component of the candidate sample component in the candidate sample vector set, based on the physical coupling matrix and combined with the gradient value of the performance prediction variance relative to the process parameter component of the candidate sample component, the coupling gain factor of the process parameter component of the candidate sample component is calculated.

[0153] S3, for each process parameter component of the candidate sample component in the candidate sample vector set, quantify the influence of the process parameter component of the candidate sample component on the parameter causal relationship diagram, and obtain the causal information value of the process parameter component of the candidate sample component.

[0154] S4. For each process parameter component of the candidate sample component in the candidate sample vector set, input the process parameter component of the candidate sample component into the physical manifold encoder to obtain the latent encoding vector of the process parameter component of the candidate sample component, and quantify the minimum difference between the latent encoding vector and the latent encoding vector of the process parameter components of other training components in the model training set to obtain the minimum spatial distance of the process parameter components of the candidate sample component.

[0155] S5. Based on the performance prediction variance, coupling gain factor, causal information value and minimum spatial distance, the comprehensive utility value of the process parameter component of the candidate sample component is calculated, and the process parameter component of the candidate sample component with the maximum comprehensive utility value is selected as the process parameter component of the training component.

[0156] S6. Obtain the true performance vector of the process parameter components of the training components, add the process parameter components of the training components, the true performance vector of the process parameter components of the training components, and the latent encoding vector to the model training set to obtain a new model training set; and train the titanium alloy mechanical property prediction model based on the new model training set to obtain the updated titanium alloy mechanical property prediction model.

[0157] Furthermore,

[0158] in, It is the index of the process parameter component of any candidate sample. It is the first Each candidate sample component contains process parameter components. It is the first The comprehensive utility value of the process parameter components of each candidate sample. It is the first The performance prediction variance of each candidate sample component's process parameter component. It is the first The coupling gain factor of the process parameter components of each candidate sample. It is the first The causal information value of the process parameter components of each candidate sample. It is the first The minimum spatial distance between the process parameter components of each candidate sample. These are the preset bandwidth parameters. These are the coupling gain weighting coefficients. It is the weighted coefficient of causal information value.

[0159] In one embodiment, such as Figure 3 A computer device is provided, comprising:

[0160] At least one processor 301, and a memory 302 communicatively connected to at least one of the processors 301: the memory stores application code executable by at least one of the processors, the application code being executed by at least one of the processors to enable at least one of the processors to perform an active learning-based method for predicting the mechanical properties of titanium alloys as described above.

[0161] Computer equipment may also include: sensor 303.

[0162] The processor 301, memory 302 and sensor 303 can be connected via a bus or other means, with the bus being an example in the figure.

[0163] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0164] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The components described as separate parts may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this disclosure according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0165] The above-described embodiments are merely illustrative of several implementation methods of the embodiments of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the embodiments of this application, and these modifications and improvements all fall within the protection scope of the embodiments of this application.

Claims

1. A method for predicting the mechanical properties of titanium alloys based on active learning, characterized in that, The method includes: Obtain a set of historical sample vectors, wherein each historical sample vector in the set includes historical composition process parameter components and labeled mechanical property components; Based on the historical sample vector set, the physical relationships characterized by the components of the historical process parameters are analyzed to obtain physical relationship data; wherein, the physical relationship data includes a physical coupling matrix and a parameter causal relationship diagram; A physical manifold encoder is constructed based on the historical sample vector set; A Gaussian process regression model is initialized to obtain an initial prediction model. Based on a preset candidate sample vector set, the physical relationship data, and the physical manifold encoder, the initial prediction model is trained to obtain a trained titanium alloy mechanical property prediction model. The titanium alloy mechanical property prediction model is used to predict the mechanical properties of titanium alloys.

2. The method according to claim 1, characterized in that, The historical composition process parameter components include at least one process parameter and at least one composition parameter; the labeled mechanical property components include at least one mechanical property parameter; and the analysis of the physical relationships represented by the historical composition process parameter components based on the historical sample vector set yields physical relationship data, including: Traverse each of the process parameters and component parameters in the historical sample vector set to form a synthetic parameter pair. For each synthetic parameter pair, use the synthetic parameter pair as the independent variable and any one of the mechanical property parameters in the labeled mechanical property components as the dependent variable to fit a local quadratic surface model of the synthetic parameter pair. For each of the synthesized parameter pairs, the local quadratic surface model is solved to obtain the coupling strength value between the synthesized parameter pair and the mechanical performance parameter; For each of the synthesized parameter pairs, the average coupling strength between the synthesized parameter and each of the mechanical performance parameters is calculated to obtain the average coupling strength value of the synthesized parameter pair; and the average coupling strength values ​​of each of the synthesized parameter pairs are integrated to obtain the physical coupling matrix. Using each of the aforementioned process parameters and each of the aforementioned component parameters as graph nodes, an initial parameter relationship graph is obtained; Based on the historical sample vector set, the relationships between the graph nodes in each of the initial parameter relationship graphs are solved to obtain the parameter causal relationship matrix. Based on the parameter causal relationship matrix, the connection edges between each of the graph nodes in the initial parameter relationship graph are constructed to obtain the parameter causal relationship graph. The physical relationship data is composed based on the physical coupling matrix and the parameter causal relationship graph.

3. The method according to claim 2, characterized in that, The process of solving the relationships between graph nodes in the initial parameter relationship graph based on the historical sample vector set to obtain the parameter causal relationship matrix includes: The number of nodes in the initial parameter relationship graph is counted to obtain the total number of nodes, and an initial adjacency matrix is ​​constructed based on the total number of nodes. Based on the historical component process parameter components in the historical sample vector set, a historical parameter matrix is ​​constructed, and the optimized value of the initial adjacency matrix is ​​calculated based on the historical parameter matrix. The expression for the optimized value is: in, It is the initial adjacency matrix. It is the optimized value of the initial adjacency matrix. It is the number of historical component process parameter components in the historical sample vector set. It is a historical parameter matrix. It is the regularization coefficient; Constrained by a preset set of parameter relationship rules, the initial adjacency matrix is ​​adjusted in the direction of reducing the optimization value until the optimization value converges to the minimum value. The initial adjacency matrix corresponding to the minimum optimization value is then used as the parameter causal relationship matrix.

4. The method according to claim 2, characterized in that, The construction of the physical manifold encoder based on the historical sample vector set includes: Based on the encoder and decoder, an initial variational autoencoder is constructed; and the historical component process parameter components in the historical sample vector set are input into the initial variational autoencoder to obtain the latent variable mean vector, latent variable variance vector and reconstructed feature vector corresponding to the historical component process parameter components. Based on the historical component process parameter components, the latent variable mean vector, latent variable variance vector, and reconstructed feature vector corresponding to the historical component process parameter components, the loss function value is calculated, and the expression of the loss function value is: in, It is the value of the loss function. It is the number of historical component process parameter components in the historical sample vector set. It is an index of any historical component's process parameter. It is the first Each historical component and process parameter component It is the first The reconstructed feature vectors corresponding to the historical component process parameter components. It is the regularization weight coefficient. It is the divergence calculation function. It is the standard normal distribution function. It is the first The vector of latent variable means corresponding to each historical component and process parameter. It is the first The variance vector of latent variables corresponding to each historical component process parameter component; The initial variational autoencoder is iteratively trained in the direction of minimizing the loss function value until a preset training termination condition is met, resulting in a trained variational autoencoder. The encoder is then extracted from the variational autoencoder as the physical manifold encoder.

5. The method according to claim 3, characterized in that, The initial prediction model is trained based on a preset candidate sample vector set, the physical relationship data, and the physical manifold encoder to obtain a trained prediction model for the mechanical properties of titanium alloys, including: Initialize the model training set, and use the initial prediction model as the initial prediction model of the titanium alloy mechanical properties prediction model. Based on the model training set, the physical relationship data, the physical manifold encoder and the initial prediction model, execute steps S1 to S6 until the preset convergence condition is met to obtain the titanium alloy mechanical properties prediction model. Steps S1 to S6 are as follows: S1, For each candidate sample component process parameter component in the candidate sample vector set, input the candidate sample component process parameter component into the titanium alloy mechanical property prediction model to obtain the performance prediction variance value of the candidate sample component process parameter component; S2, for each process parameter component of the candidate sample component in the candidate sample vector set, based on the physical coupling matrix and combined with the gradient value of the performance prediction variance value relative to the process parameter component of the candidate sample component, the coupling gain factor of the process parameter component of the candidate sample component is calculated. S3, for each process parameter component of the candidate sample component in the candidate sample vector set, quantify the influence of the process parameter component of the candidate sample component on the parameter causal relationship diagram, and obtain the causal information value of the process parameter component of the candidate sample component; S4, for each of the process parameter components of the candidate sample components in the candidate sample vector set, the process parameter component of the candidate sample components is input into the physical manifold encoder to obtain the latent coding vector of the process parameter component of the candidate sample components, and the minimum difference between the latent coding vector and the latent coding vector of the process parameter components of other training components in the model training set is quantified to obtain the minimum spatial distance of the process parameter components of the candidate sample components. S5. Based on the performance prediction variance, the coupling gain factor, the causal information value, and the minimum spatial distance, calculate the comprehensive utility value of the process parameter component of the candidate sample component, and select the process parameter component of the candidate sample component with the maximum comprehensive utility value as the process parameter component of the training component. S6, obtain the true performance vector of the process parameter component of the training component, add the process parameter component of the training component, the true performance vector of the process parameter component of the training component, and the latent encoding vector to the model training set to obtain a new model training set; and train the titanium alloy mechanical property prediction model based on the new model training set to obtain the updated titanium alloy mechanical property prediction model.

6. The method according to claim 5, characterized in that, The expression for the comprehensive utility value is: in, It is the index of the process parameter component of any candidate sample. It is the first Each candidate sample component contains process parameter components. It is the first The comprehensive utility value of the process parameter components of each candidate sample. It is the first The performance prediction variance of each candidate sample component's process parameter component. It is the first The coupling gain factor of the process parameter components of each candidate sample. It is the first The causal information value of the process parameter components of each candidate sample. It is the first The minimum spatial distance between the process parameter components of each candidate sample. These are the preset bandwidth parameters. These are the coupling gain weighting coefficients. It is the weighted coefficient of causal information value.

7. A device for predicting the mechanical properties of titanium alloys based on active learning, characterized in that, The device includes: The data acquisition module is used to acquire a historical sample vector set, wherein each historical sample vector in the historical sample vector set includes historical composition process parameter components and labeled mechanical property components. The physical relationship calculation module is used to analyze the physical relationships characterized by the components of the historical process parameters based on the historical sample vector set, and obtain physical relationship data; wherein, the physical relationship data includes a physical coupling matrix and a parameter causal relationship graph; An autoencoder construction module is used to construct a physical manifold encoder based on the historical sample vector set; The model training module is used to initialize the Gaussian process regression model to obtain an initial prediction model, and to train the initial prediction model based on a preset candidate sample vector set, the physical relationship data, and the physical manifold encoder to obtain a trained titanium alloy mechanical property prediction model; the titanium alloy mechanical property prediction model is used to predict the mechanical properties of titanium alloys.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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