Physical-data dual-drive large tube plate mechanical property prediction method

Abstract

The invention relates to a physical-data dual-driven large-scale tube plate mechanical property prediction method, which comprises the following steps of: fusing multi-source data to construct a data set, establishing a symbol regression model, embedding physical constraints in genetic operation to enable a generated expression to accord with a physical rule, and introducing a dynamic complexity control item into a fitness function to predict the mechanical property of a large-scale tube plate. It is ensured that the generated mathematical expression has high precision, physical rationality and conciseness; and finally, outputting an explicit calculation formula of the relationship between the mechanical properties and the input parameters and a mechanical property predicted value. According to the method, through multi-source data fusion and physical constraint symbol regression, data-mechanism dual drive of tube plate mechanical property prediction is achieved, the precision, efficiency, compliance and cost control are substantially improved, the generated expression is high in interpretability, the supervision requirement of the high-safety field can be met, and the method is suitable for popularization and application. And a reliable intelligent decision-making tool is provided for high-end equipment manufacturing.

Description

Technical Field

[0001] This invention relates to the field of predicting the mechanical properties of large forging materials, and specifically to a method for predicting the mechanical properties of large tube sheets driven by both physical and data principles. Background Technology

[0002] With the widespread application of large pressure vessels in nuclear power, petrochemical and other fields, the accurate prediction of the mechanical properties (such as yield strength, tensile strength, etc.) of tube sheets, as core pressure-bearing components, has become the key to ensuring the safety and reliability of equipment.

[0003] Currently, the industry typically employs experimental methods for destructive testing of large tube sheets. However, in practical applications, large tube sheets must withstand extreme conditions (high temperature, high pressure, corrosive media). Traditional trial-and-error methods require preparing numerous samples and conducting destructive tests (such as tensile, impact, and fatigue tests), with a single full-performance test costing tens of thousands of yuan, severely hindering the efficiency of new material development. For thick plate materials, layered performance testing (such as 1 / 4 thickness or core sampling) further exacerbates resource consumption and makes online dynamic optimization of process parameters impossible. Existing mechanical property predictions largely rely on empirical formulas based on physical metallurgy (such as the Hall-Petch formula and hybrid strengthening models), whose modeling process requires pre-assuming mathematical forms (such as linear superposition or power-law relationships), making it difficult to capture the complex nonlinear laws under the coupling of multiple process parameters. Simultaneously, for novel alloy materials or special processing techniques (such as gradient heat treatment), the generalization ability of empirical formulas significantly decreases, requiring frequent experimental verification, leading to extended R&D cycles and soaring costs.

[0004] In recent years, while machine learning-based prediction methods (such as backpropagation neural networks and convolutional neural networks) have improved accuracy, their "black box" nature means that the models cannot output explicit mathematical expressions or physical logic relationships, making it difficult for engineers to verify whether the prediction results conform to the basic principles of materials science. In fields with high safety requirements, such as nuclear power, prediction models lacking transparency often fail to pass regulatory reviews and cannot guide the reverse optimization of process parameters (e.g., they cannot analyze the weights of key influencing factors).

[0005] For example, Chinese patent CN112100745A discloses a method for predicting the mechanical properties of automotive beam steel based on LDA theory. This method constructs a dataset from a large amount of historical production data generated during the production of hot-rolled high-strength steel. After establishing a mechanical property prediction model, the characteristic attribute parameters (process and composition parameters) of the predicted data sample set are input into the mechanical property prediction model to obtain the mechanical properties of the predicted samples. This effectively improves the efficiency of mechanical property testing, reduces testing costs, and achieves high efficiency and convenience in the testing of automotive beam steel. However, this prediction model lacks transparency and has insufficient interpretability.

[0006] Furthermore, with the development of machine learning, Wang et al. comprehensively used multiple algorithms to predict the mechanical properties of large forgings made of die steel. Taking hot-work die steel as the research object, they conducted heat treatment experiments and mechanical property tests to obtain a dataset of the mechanical properties of large forgings made of die steel after heat treatment. This dataset was first preprocessed to obtain a high-quality mechanical property dataset; then, importance analysis was used to filter the input parameters, removing weakly correlated variables to reduce model complexity; subsequently, random forest, decision tree, and backpropagation (BP) neural network algorithms were constructed, and the prediction accuracy of each algorithm was compared to select the optimal algorithm model. The algorithm was then validated and applied. However, this data-driven mechanical property prediction model struggles to capture the abstract and implicit cross-information in the data, and the model is a "black box," unable to accurately express the relationship between mechanical properties and input parameters. Summary of the Invention

[0007] To address the issues of insufficient model interpretability and low utilization of multi-source data in existing technologies, this invention proposes a physical-data dual-driven method for predicting the mechanical properties of large tube sheets. By using symbolic regression to establish the relationship between material composition, process parameters, and mechanical properties, and by integrating multi-source data and embedding physical constraint rules, this method can effectively improve the efficiency of mechanical property testing, reduce testing costs, and achieve high efficiency and convenience in the mechanical property testing of large tube sheets.

[0008] To achieve the above objectives, the technical solution adopted by this invention is: a physical-data dual-driven method for predicting the mechanical properties of large tube sheets, the method comprising the following steps:

[0009] S1: Obtain historical data on material composition, process parameters, microstructure characteristics and measured mechanical properties of large tube sheets, and construct a dataset and symbol library. The symbol library includes input variables, operation operators and constants.

[0010] S2: Preprocess the input variables in the symbol library, including missing value imputation, outlier handling, and normalization;

[0011] S3: Construct a symbolic regression model based on an improved genetic programming algorithm. Based on the input variables, generate an initial population. On the basis of the initial population, select nodes from the symbol library to perform crossover, mutation, and selection operations, and iteratively optimize the formula tree.

[0012] S4: In crossover and mutation operations, the physical rationality of the formula is verified in real time; a physical rule constraint module is set, which includes mechanical constraints, thermodynamic constraints, and material constitutive constraints; the generated formula tree is scanned for physical rules, scanning all operator nodes. If they do not conform to the physical rule constraints, the non-conforming parts are directly replaced according to independent specific rules to make them conform to the physical rules before adaptive function verification is performed; finally, the explicit calculation formula and predicted value of the relationship between mechanical properties and input parameters are output.

[0013] Further, in step S1, the input variables in the symbol library are the material composition, process parameters, microstructure characteristics, and measured mechanical properties of the large tube sheet; the arithmetic operators include addition operators, subtraction operators, multiplication operators, division operators, trigonometric function operators, exponential operators, and squaring operators.

[0014] Furthermore, in step S2, data preprocessing specifically includes the following steps:

[0015] S2.1 Missing value imputation: A collaborative filtering algorithm based on material gene similarity is used to impute missing fields using data of similar alloys;

[0016] S2.2 Outlier Handling: First, hierarchical clustering is performed on the dataset after missing values ​​are filled. Based on hierarchical clustering, different outlier removal criteria are selected according to the number of tube sheet data in the same cluster. That is, when the number of samples in the cluster is greater than the set threshold, the 3σ criterion is used to remove outliers in the cluster; otherwise, the Grubbs criterion is used to remove outliers.

[0017] S2.3 Normalization: Standardize parameters with different dimensions to ensure data consistency.

[0018] Furthermore, in step S2.1, the formula for completing missing fields using data of similar alloys is:

[0019]

[0020] In the formula, x 缺失 The missing values ​​to be filled are sim, the component similarity function is k, the number of nearest neighbors is k, and C is k. i Let C be the composition of the i-th known complete alloy sample. 缺失 For the composition of alloy samples with missing fields, x i C i The corresponding x in 缺失 The specific values ​​of missing components of the same attribute.

[0021] Further, in step S2.2, before removing outliers, a hierarchical clustering method based on Mahalanobis distance is used to cluster the data. Each sample after filling in missing values ​​is initialized as an independent cluster. The Mahalanobis distance between two clusters is calculated iteratively, and clusters with the smallest Mahalanobis distance value are continuously merged. When the key components and process parameters of samples within the same cluster show high similarity, they are determined to be production data under the same procedure. The Mahalanobis distance dM is calculated using the following formula:

[0022]

[0023] In the formula, x is the difference matrix between the two objects. Σ is the mean vector; Σ is the covariance matrix.

[0024] Furthermore, the specific steps for model construction in step S3 are as follows:

[0025] Step 3.1 Dataset partitioning: Input the feature parameters obtained after data preprocessing, randomly partition 80% of the data as the training set and 20% of the data as the test set, and standardize all data.

[0026] Step 3.2 Model Construction: Establish a symbolic regression algorithm model based on improved genetic programming. Using a defined set of operators, input variables, and constants, generate an initial population and randomly generate 5000 initial formula trees, each with a depth of ≤5 levels. Then, perform crossover and mutation operations. The crossover operation involves selecting two formula trees from the parent population and randomly swapping their subtrees to generate offspring. The mutation operation involves randomly replacing nodes in the formula trees, including operators, variables, and constants.

[0027] Step 3.3: An adaptive penalty mechanism is used to balance the complexity and accuracy of the expression. The fitness function is designed as follows:

[0028] Fitness = MSE + λ(t)·N terms • Depth; where the penalty factor λ(t) decays over time, and MSE is the mean squared error between the model prediction and the experimental value; N terms is the number of formula terms; Depth is the depth of the formula tree; the intensity of the complexity penalty is controlled by dynamically adjusting the penalty factor, and the fitness function gradually reduces the complexity weight as iterative optimization progresses.

[0029] Further, in step S3.1, the input variables include material composition parameters and process parameters, specifically the material composition C content, Si content, Mn content, P content, S content, Al content, Ti content, Nb content, Cr content and N content; the processing parameters include heat treatment temperature and pre-forging heating temperature; the constant term c is defined as having a limited range of [-10, 10].

[0030] Furthermore, the punishment factor Where λ0 is the initial penalty intensity, T0 is the decay period, and t is the current iteration number.

[0031] Furthermore, in step S4, the mechanical constraint is: to prohibit the generation of asymmetric stress terms that violate Saint-Venant's principle;

[0032] Thermodynamic constraint: The energy density term U must satisfy...

[0033] The constitutive constraint of the material is: yield strength σ s The elastic modulus E must satisfy σ s ≤0.01E.

[0034] Furthermore, the independent specific rule is as follows:

[0035] If asymmetric stress is detected, a subtree replacement is triggered, replacing the asymmetric stress term with a symmetric one;

[0036] If the generating formula contains an energy density term U = k0T + C, and k0 > 0, then check the sign of its derivative. If the derivative of the energy density term does not conform to the formula... When the energy density term is replaced with a negative function U = k0e -T +C, where U represents energy density, k0 is a coefficient, T is temperature, and C is a constant;

[0037] If the yield strength σ s The elastic modulus E does not conform to σ s If ≤0.01E, then replace it with a threshold constraint: max(0,σ) s -0.01E)·k1, where k1 is a correction coefficient with a value between 0 and 1, used to reduce yield strength values ​​that exceed the reasonable range to a reasonable range.

[0038] The beneficial effects of the present invention using the above technical solution are as follows:

[0039] I. Multi-source data fusion and high-precision prediction: This invention integrates material composition, process parameters, microstructure characteristics and experimental data to construct a cross-scale training set, which significantly improves the model's generalization ability.

[0040] II. Physically Constrained Interpretable Models: By embedding physical rules such as Saint-Venant's principle and energy conservation, the generated mathematical expressions combine high precision with scientific compliance, can clearly reveal physical relationships, meet the mandatory review requirements for model transparency in fields such as nuclear power and petrochemicals, and support process reverse optimization.

[0041] Third, R&D costs and resource consumption are significantly reduced: By using symbolic regression to recommend the optimal component-process combination, the number of trial and error experiments is reduced, and the material development cost is lowered.

[0042] IV. Promoting the research on material mechanisms and the iteration of standards: The expressions generated by the method of this invention reveal previously unknown physical mechanisms and supplement traditional strengthening theories.

[0043] In summary, this invention achieves a leap from "experience-driven" to "data-mechanism dual-driven" prediction of tube sheet mechanical properties through multi-source data fusion and physical constraint symbolic regression. It breaks through existing technical bottlenecks in terms of accuracy, efficiency, compliance, and cost control, providing a reliable intelligent decision-making tool for high-end equipment manufacturing. Attached Figure Description

[0044] Figure 1 This is an overall flowchart of the large tube sheet mechanical property prediction model method of the present invention;

[0045] Figure 2 This is a schematic diagram illustrating the principle of the symbolic regression model based on the improved genetic algorithm of this invention;

[0046] Figure 3 This is a diagram showing the accuracy of the room temperature yield strength prediction in an embodiment of the present invention.

[0047] Figure 4 This is a diagram showing the accuracy of high-temperature yield strength prediction in an embodiment of the present invention.

[0048] Figure 5 This is a diagram illustrating the tensile strength prediction accuracy of an embodiment of the present invention.

[0049] Figure 6 This is a graph showing the elongation prediction accuracy of an embodiment of the present invention. Detailed Implementation

[0050] The present invention will now be described more completely and clearly with reference to the accompanying drawings and specific embodiments.

[0051] In the embodiments, the large tube sheet mechanical property prediction method based on symbolic regression model proposed in this invention is used to establish the prediction formula for the mechanical properties of large tube sheets in large pressure vessels in nuclear power, petrochemical and other fields, and to predict the mechanical properties of large tube sheets, thereby demonstrating the performance advantages of the method of this invention.

[0052] like Figure 1 As shown, the method for predicting the mechanical properties of large tube sheets based on a symbolic regression model specifically includes the following steps.

[0053] Step S1: Obtain historical data on the material composition, process parameters, and mechanical properties of large tube sheets, and determine the dataset and symbol library.

[0054] Step S1.1: Based on the large amount of production and measured data obtained from papers and actual production, a dataset of fatigue tests for large tube sheet materials is constructed, and a cross-scale database is built to cover the entire chain of information from material design to manufacturing to testing; the historical data includes material composition parameters, process parameters, microstructure characteristics, and measured mechanical properties.

[0055] Step S1.2: Determine the symbol library and output of the symbolic regression model based on the large tube sheet material mechanical property dataset and empirical formulas for mechanical properties. The symbol library includes the following nodes: input variables, operation operators, and constants.

[0056] Let the input variables be material composition parameters, process parameters, microstructure characteristics, and measured mechanical properties. Specifically, the material composition parameters include: C content, Si content, Mn content, P content, S content, Al content, Ti content, Nb content, Cr content, and N content; the process parameters include: pre-forging heating temperature, forging ratio, and heat treatment temperature; the microstructure characteristics include: grain size and phase ratio; and the measured mechanical property data include: yield strength σ. s Tensile strength σ b Elongation δ.

[0057] The operators involved in the symbolic regression model mainly include binary operators {+,-,×,÷} and unary operators {sin,cos,log,exp,sqrt}.

[0058] The symbol library is represented as {x i ,operator,c},x i Here, the input material composition parameters and process parameters are represented, operator represents all operation operators, and c represents the constant node in the expression; the expression sequence nodes are all sampled from the symbol library.

[0059] The output of the symbolic regression model is the mechanical performance prediction formula and mechanical performance data, including the physical model formula for mechanical performance prediction, the predicted mechanical performance values ​​(with confidence intervals), the ranking of key influencing factors, and process optimization suggestions.

[0060] Step S2: Perform data preprocessing on the data in the dataset to suit the symbolic regression model.

[0061] Step S2.1: Perform data cleaning on the dataset;

[0062] Missing value imputation: For tube sheet data parameters that are missing or have identical data, the data for that parameter is removed. For missing general parameters, a collaborative filtering algorithm based on material gene similarity is used to fill in the missing fields using data of similar alloys, as shown in the following formula:

[0063]

[0064] In the formula, x 缺失 The missing values ​​to be filled are sim, the component similarity function is k, the number of nearest neighbors is k, and C is k. i Let C be the composition of the i-th known complete alloy sample. 缺失 For the composition of alloy samples with missing fields, x i C i The corresponding x in 缺失 The specific values ​​of missing components of the same attribute.

[0065] Step S2.2: Outlier handling. Hierarchical clustering is performed on the dataset after missing value imputation. Based on this hierarchical clustering, outlier removal is performed. Different outlier removal criteria are selected according to the number of tube sheet data points in the same cluster. Specifically, when the number of samples in a cluster exceeds a set threshold, the 3σ criterion is used to remove outliers from the cluster; otherwise, the Grubbs criterion is used.

[0066] Step S2.2.1 addresses the issue of outliers and redundant values ​​in the data by proposing a hierarchical clustering solution based on Mahalanobis distance. Each sample, after filling in missing values, is initialized as an independent cluster. The Mahalanobis distance between two clusters is iteratively calculated, and clusters with the smallest Mahalanobis distance are continuously merged (i.e., if the distance between cluster 1 and cluster 2 is the shortest Mahalanobis distance among all different clusters, then cluster 1 and cluster 2 are merged); Mahalanobis distance d M It can be obtained by the following formula (2):

[0067]

[0068] In the formula, x is the difference matrix between the two objects; Σ is the mean vector; Σ is the covariance matrix.

[0069] By setting an appropriate number of clusters, samples can be divided into different clusters to achieve data classification. When the key components and process parameters of samples within the same cluster are highly similar, they can be identified as production data under the same procedure.

[0070] Step S2.2.2: Based on hierarchical clustering, different outlier removal criteria are selected according to the number of tube sheet data in the same cluster. That is, when the number of samples in the cluster is greater than the set threshold (set to 30 in this embodiment), i.e., large sample mode, the 3σ criterion is used to remove outliers in the cluster. Otherwise, in small sample mode, the Grubbs criterion is used to remove outliers.

[0071] The 3σ criterion establishes the exclusion boundary based on the normal distribution assumption. Its mathematical expression is: probability P(|x-μ|>3σ), 0.003, where μ is the mean of a certain mechanical performance element, and σ is the variance of that mechanical performance element. The specific calculation formula is:

[0072]

[0073]

[0074] Therefore, when the mechanical property error of a certain tube sheet material is P = x i -μ can be considered an outlier and removed when it satisfies the following formula (5).

[0075] |P|=∣x i -μ∣>3σ (5)

[0076] The Grubbs criterion compares a statistic with a critical value: if G > G(n, α), then the corresponding element is considered an outlier, where G is the Grubbs critical value, n is the number of elements, and α is the significance level.

[0077] The formula for calculating the Grubbs critical value G is as follows:

[0078]

[0079] In the formula, M is the median of the n data sets.

[0080] Step 2.3: Normalization.

[0081] Considering that the input temperature and element content usually have physical units, such as °C, in order to unify the physical units on both sides of the expression, this invention introduces dimensionless preprocessing to normalize various types of data and transform them into data within the (0,1) interval. The normalization formula is as follows.

[0082]

[0083] In the formula, x max For x i The maximum value in the parameter data, x min For x i The minimum value in the parameter data, x i ′ represents the normalized value.

[0084] Step S3: Modeling using symbolic regression method. Using defined operators and preprocessed data, establish an adaptive symbolic regression model driven by physical constraints.

[0085] The symbolic regression modeling method specifically includes the following steps:

[0086] Step S3.1: Dataset partitioning: Input the feature parameters obtained after data preprocessing, randomly partition 80% of the data as the training set and 20% of the data as the test set, and standardize all the data.

[0087] Step 3.2: Model construction. Using the determined operators and preprocessed data, a model based on the improved genetic programming symbolic regression algorithm is established. The optimal function expression is obtained from the output of the symbolic regression model, and the calculation method of mechanical performance parameters with respect to material property parameters is obtained. The calculation results of mechanical performance parameters are obtained using this calculation method.

[0088] In the symbolic regression model based on an improved genetic programming algorithm, each randomly generated expression is represented as an independent binary tree, where the root node represents a function or mathematical operator, and the leaf nodes contain variables or constants. A schematic diagram of the model is shown below. Figure 2 As shown. The symbolic regression model achieves physical rule embedding through an improved genetic programming framework. The specific steps of the genetic programming algorithm are as follows:

[0089] S3.2.1 Based on the set of basic operators {+,-,×,÷,sin,cos,log,exp} determined in step S1, the input variables and constant term c, generate an initial population and randomly generate 5000 initial formula trees, each with a depth of ≤5 levels, to ensure that the initial complexity is controllable.

[0090] Specifically, the input variables include material composition parameters and process parameters. The material composition includes: C content, Si content, Mn content, P content, S content, Al content, Ti content, Nb content, Cr content, and N content. The processing parameters include: heat treatment temperature and pre-forging heating temperature. The constant term c is limited to the range of [-10, 10] to avoid numerical explosion.

[0091] Step S3.2.2: Based on the initial population, select nodes from the symbol library to perform crossover, mutation, selection and other operations.

[0092] In genetic algorithms, the crossover operation involves selecting two formula trees from the parent population, randomly swapping their subtrees to generate offspring. After the crossover, the offspring are checked to see if they violate physical rules; if so, a new crossover point is selected.

[0093] The mutation operation in the genetic algorithm randomly replaces nodes in the formula tree, including operators, variables, and constants; after mutation, the offspring are checked to see if they violate physical rules, and if they do, the mutation is rolled back.

[0094] Step 3.3: Set up an adaptive penalty mechanism.

[0095] To prevent overfitting, an adaptive penalty mechanism is used to balance the complexity and accuracy of the expression; the fitness function is designed as follows:

[0096] Fitness = MSE + λ(t)·N terms •Depth (8)

[0097] In the formula, λ(t) is the penalty factor, which decays with time. (λ0 = 0.1, T0 = 1000); t is the current iteration number, which decays exponentially with the iteration number; T0 is the decay period; MSE is the mean square error between the model prediction and the experimental value; N terms λ is the number of formula terms; Depth is the depth of the formula tree (a measure of complexity); the intensity of the complexity penalty is controlled by dynamically adjusting the penalty factor λ(t), and the fitness function gradually reduces the complexity weight as iterative optimization progresses.

[0098] Step 4: Based on the improved genetic programming symbolic regression algorithm, construct a physical rule constraint module to build a formula model, scan all operator nodes, and impose physical rule constraints on them. If the physical rule constraints are not met, replace the non-compliant parts directly according to independent specific rules to make them conform to the physical rules, and then perform adaptive function verification. Finally, output the explicit calculation formula and predicted value of the relationship between mechanical properties and input parameters.

[0099] The improved genetic programming framework involves real-time verification of the physical rationality of formulas through physical rules during genetic operations (crossover, mutation). These physical rules include the following categories:

[0100] Mechanical constraints: The generation of asymmetric stress terms (such as σ) that violate Saint-Venant's principle is prohibited. xy ≠σ yx );

[0101] Thermodynamic constraint: The energy density term U must satisfy...

[0102] Constitutive constraints of materials: yield strength σ s The elastic modulus E satisfies σ s ≤0.01E.

[0103] After generating a new formula tree through crossover or mutation, all operator nodes are scanned. If they do not conform to the physical rules, they are replaced. Specifically:

[0104] If asymmetric stress such as σ is detected xy ≠σ yx This triggers a subtree replacement, correcting it to the symmetric form σ. xy =σ yx .

[0105] If the generating formula contains an energy density term U = k0T + C, and k0 > 0, then check the sign of its derivative. If the derivative of the energy density term does not conform to the formula... When the energy density term is replaced with a negative function U = k0e -T +C; where U represents energy density, k0 is a coefficient, T is temperature, and C is a constant.

[0106] If the yield strength σ is in the calculation result of the formula s The elastic modulus E does not meet the threshold σ s If ≤0.01E, then replace it with a threshold constraint: max(0,σ) s -0.01E)·k1, where k1 is a correction factor that is a constant between 0 and 1, used to reduce yield strength values ​​that are outside the reasonable range to a reasonable range.

[0107] The model building process of this invention involves necessary hyperparameter settings. Table 1 shows the hyperparameter settings for the overall structural constraints of the expression.

[0108] Table 1 Hyperparameter Setting Data

[0109] Finally, the formula tree that best fits the output to the data is taken as the model's best prediction result. Taking into account both the data fitting ability and physical interpretability of the output formula, the formula with the best performance is selected for each output parameter.

[0110] according to Figure 3-6 The statistical analysis chart of the accuracy of the mechanical property prediction results shows that the method described in this invention has high accuracy in predicting yield strength at room temperature, yield strength at high temperature, tensile strength, and elongation.

[0111] This invention, through physical constraint embedding and dynamic complexity control, enables the symbolic regression model to generate expressions that conform to the laws of materials science while ensuring high accuracy, providing an interpretable and verifiable theoretical basis for process optimization.

[0112] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for predicting the mechanical properties of large tube sheets driven by both physical and data principles, characterized in that, The method includes the following steps: S1: Obtain historical data on material composition, process parameters, microstructure characteristics and measured mechanical properties of large tube sheets, and construct a dataset and symbol library. The symbol library includes input variables, operation operators and constants. S2: Preprocess the input variables in the symbol library, including missing value imputation, outlier handling, and normalization; S3: Construct a symbolic regression model based on an improved genetic programming algorithm. Based on the input variables, generate an initial population. On the basis of the initial population, select nodes from the symbol library to perform crossover, mutation, and selection operations, and iteratively optimize the formula tree. S4: In crossover and mutation operations, the physical rationality of the formula is verified in real time; a physical rule constraint module is set, which includes mechanical constraints, thermodynamic constraints, and material constitutive constraints; the generated formula tree is scanned for physical rules, scanning all operator nodes. If they do not conform to the physical rule constraints, the non-conforming parts are directly replaced according to independent specific rules to make them conform to the physical rules before adaptive function verification is performed; finally, the explicit calculation formula and predicted value of the relationship between mechanical properties and input parameters are output.

2. The method for predicting the mechanical properties of large tube sheets driven by both physical and data principles, as described in claim 1, is characterized in that... In step S1, the input variables in the symbol library are the material composition, process parameters, microstructure characteristics, and measured mechanical properties of the large tube sheet; the arithmetic operators include addition, subtraction, multiplication, division, trigonometric function, exponentiation, and squaring operators.

3. The method for predicting the mechanical properties of large tube sheets driven by both physical and data principles, as described in claim 1, is characterized in that... In step S2, data preprocessing specifically includes the following steps: S2.1 Missing value imputation: A collaborative filtering algorithm based on material gene similarity is used to impute missing fields using data of similar alloys; S2.2 Outlier Handling: First, hierarchical clustering is performed on the dataset after missing values ​​are filled. Based on hierarchical clustering, different outlier removal criteria are selected according to the number of tube sheet data in the same cluster. That is, when the number of samples in the cluster is greater than the set threshold, the 3σ criterion is used to remove outliers in the cluster; otherwise, the Grubbs criterion is used to remove outliers. S2.3 Normalization: Standardize parameters with different dimensions to ensure data consistency.

4. The method for predicting the mechanical properties of large tube sheets driven by both physical and data principles, as described in claim 3, is characterized in that... In step S2.1, the formula for completing missing fields using data of similar alloys is: In the formula, x 缺失 The missing values ​​to be filled are sim, the component similarity function is k, the number of nearest neighbors is k, and C is k. i Let C be the composition of the i-th known complete alloy sample. 缺失 For the composition of alloy samples with missing fields, x i C i The corresponding x in 缺失 The specific values ​​of missing components of the same attribute.

5. The method for predicting the mechanical properties of large tube sheets driven by both physical and data principles, as described in claim 3, is characterized in that... In step S2.2, before removing outliers, a hierarchical clustering method based on Mahalanobis distance is used to cluster the data. Each sample after filling in missing values ​​is initialized as an independent cluster. The Mahalanobis distance between two clusters is calculated iteratively, and clusters with the smallest Mahalanobis distance value are continuously merged. When the key components and process parameters of samples within the same cluster show high similarity, they are determined to be production data under the same procedure; Mahalanobis distance d M It can be obtained using the following formula: In the formula, x is the difference matrix between the two objects. Σ is the mean vector; Σ is the covariance matrix.

6. The method for predicting the mechanical properties of large tube sheets driven by both physical and data principles, as described in claim 1, is characterized in that... The specific steps for building the S3 model are as follows: Step 3.1 Dataset partitioning: Input the feature parameters obtained after data preprocessing, randomly partition 80% of the data as the training set and 20% of the data as the test set, and standardize all data. Step 3.2 Model Construction: Establish a symbolic regression algorithm model based on improved genetic programming. Using a defined set of operators, input variables, and constants, generate an initial population and randomly generate 5000 initial formula trees, each with a depth of ≤5 levels. Then, perform crossover and mutation operations. The crossover operation involves selecting two formula trees from the parent population and randomly swapping their subtrees to generate offspring. The mutation operation involves randomly replacing nodes in the formula trees, including operators, variables, and constants. Step 3.3: An adaptive penalty mechanism is adopted to balance the complexity and accuracy of the expression. The fitness function is designed as: Fitness = MSE + λ(t)·N terms • Depth; where the penalty factor λ(t) decays over time, and MSE is the mean squared error between the model prediction and the experimental value; N terms is the number of formula terms; Depth is the depth of the formula tree; the intensity of the complexity penalty is controlled by dynamically adjusting the penalty factor, and the fitness function gradually reduces the complexity weight as iterative optimization progresses.

7. The method for predicting the mechanical properties of large tube sheets driven by both physical and data principles, as described in claim 6, is characterized in that... In step S3.1, the input variables include material composition parameters and process parameters, specifically the material composition C content, Si content, Mn content, P content, S content, Al content, Ti content, Nb content, Cr content and N content; the processing parameters include heat treatment temperature and pre-forging heating temperature; the constant term c is defined as having a limited range of [-10, 10].

8. The method for predicting the mechanical properties of large tube sheets driven by both physical and data principles, as described in claim 6, is characterized in that... Punishment factor Where λ0 is the initial penalty intensity, T0 is the decay period, and t is the current iteration number.

9. The method for predicting the mechanical properties of large tube sheets driven by both physical and data principles, as described in claim 1, is characterized in that... In step S4, the mechanical constraint is: to prohibit the generation of asymmetric stress terms that violate Saint-Venant's principle; Thermodynamic constraint: The energy density term U must satisfy... The constitutive constraint of the material is: yield strength σ s The elastic modulus E must satisfy σ s ≤0.01E.

10. The method for predicting the mechanical properties of large tube sheets driven by both physical and data principles, as described in claim 9, is characterized in that... The specific independent rule is: If asymmetric stress is detected, a subtree replacement is triggered, replacing the asymmetric stress term with a symmetric one; If the generating formula contains an energy density term U = k0T + C, and k0 > 0, then check the sign of its derivative. If the derivative of the energy density term does not conform to the formula... When the energy density term is replaced with a negative function U = k0e -T +C, where U represents energy density, k0 is a coefficient, T is temperature, and C is a constant; If the yield strength σs and the elastic modulus E do not conform to σ s If ≤0.01E, then replace it with a threshold constraint: max(0,σ) s -0.01E)·k1, where k1 is a correction coefficient with a value between 0 and 1, used to reduce yield strength values ​​that exceed the reasonable range to a reasonable range.

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