Ship plate high-strength steel material composition design method based on multi-objective black box optimization

Abstract

The application discloses a ship plate high-strength steel material composition design method based on multi-target black box optimization, relates to the field of metal material design, and collects ship plate high-strength steel historical data to obtain a standard semi-structured data set through alignment and cleaning treatment; based on the data set, optimization targets, decision variables and constraint conditions are determined, and a multi-target optimization model is constructed; a mechanical property prediction model integrating multiple performances is obtained through machine learning algorithm training; an optimal solution set is obtained through iterative calculation of a reference vector guided multi-target optimization algorithm, and a final composition design scheme is selected by combining target steel grade service scenarios and assigning weights, so that the complex mapping relationship of composition-process-performance is accurately quantified, the strength, toughness, weldability and corrosion resistance are simultaneously optimized to match service requirements, the optimization algorithm considers global exploration and local development, the optimal solution under multiple constraints is efficiently obtained, manual experience derivation is not needed, and the composition design can be popularized to other high-strength steels or special steels.

Description

Technical Field

[0001] This application relates to the field of metal material design technology, and in particular to a method for designing the composition of high-strength steel for ship plates based on multi-objective black-box optimization. Background Technology

[0002] With the increasing demand for high-performance structural steel in the shipbuilding industry, high-strength low-alloy steels for ships (such as AH36) must meet multiple performance requirements during actual service, including low-temperature impact toughness, high weldability, and resistance to seawater corrosion. Their material properties directly affect the safety and lifespan of the hull. The performance of steel materials is determined by both composition and processing, with chemical composition design being a crucial step. In related technologies, composition design methods mainly rely on three traditional approaches: empirical formulas, experimental design, and computational simulation. However, these methods have significant limitations when dealing with multi-indicator nonlinear coupling.

[0003] In related technologies, machine learning and multi-objective optimization techniques have been introduced into the field of materials design. For example, CN115579091A discloses a multi-performance collaborative optimization method for high-entropy alloy composition design based on machine learning. It establishes a performance prediction model using historical data and utilizes the NSGA-II algorithm to maximize performance. CN118571370A proposes a low-cost composition design optimization method for high-strength steel used in automobiles. It constructs a mechanical performance prediction model based on historical data and combines empirical formulas and grid search to locate the optimal solution. CN120048403A involves a titanium alloy composition optimization design method that uses random forests to characterize the composition-performance relationship and performs genetic operations based on composition priority. However, the applicant recognizes that existing composition design methods overemphasize maximizing the mechanical properties of materials and cannot accurately match actual application scenarios. Although machine learning techniques have been introduced into materials design, machine learning models are mostly trained on limited historical data, resulting in weak generalization ability. Moreover, traditional optimization algorithms (such as genetic algorithms) converge slowly in complex design spaces and struggle to obtain uniformly distributed Pareto solutions within a finite number of iterations, leading to extended design cycles and increased development costs. Summary of the Invention

[0004] In view of this, this application provides a method for designing the composition of high-strength steel for ship plates based on multi-objective black-box optimization. The main purpose is to solve the problems in existing ship plate steel composition design methods, such as the disconnect between the optimization objective and the actual service scenario, insufficient generalization ability of the prediction model due to data limitations, and the low search efficiency and difficulty in obtaining high-quality Pareto solution sets of traditional optimization algorithms in complex spaces.

[0005] According to the first aspect of this application, a method for designing the composition of high-strength steel for ship plates based on multi-objective black-box optimization is provided, the method comprising: Historical data of high-strength steel materials for ship plates collected from the steel plant's production and manufacturing management system is obtained. The historical data of high-strength steel materials for ship plates is then aligned and cleaned to obtain a standard semi-structured dataset. The data includes product specification data, chemical composition data, process parameter data, and performance index data. Based on the standard semi-structured dataset, the optimization objective, decision variables, and constraints of the target steel grade are determined. A multi-objective optimization model of the target steel grade is constructed using the optimization objective, decision variables, and constraints. The optimization objective includes maximizing yield strength, maximizing low-temperature impact energy, and minimizing the weld crack sensitivity index. The decision variables include chemical composition data and process parameter data. The constraints include performance constraints, element content range constraints, process parameter constraints, and corrosion resistance index constraints. The standard semi-structured dataset is trained using machine learning algorithms to obtain the mechanical property prediction model of the target steel grade, which integrates the yield strength prediction model, tensile strength prediction model, and low-temperature impact energy prediction model. A reference vector-guided multi-objective optimization algorithm is used to iteratively calculate the multi-objective optimization model and the mechanical performance prediction model to obtain the optimal solution set. Based on the service scenarios of the target steel grade, weights are assigned, and a high-strength steel material composition design scheme for the target steel grade is selected from the optimal solution set.

[0006] By employing the above technical solutions, the technical solutions provided in the embodiments of this application have at least the following advantages: This application provides a method for designing the composition of high-strength ship plate materials based on multi-objective black-box optimization. First, historical data on product specifications, chemical composition, process parameters, and performance indicators of high-strength ship plate materials are collected from the steel plant's production and manufacturing management system. This data is then aligned and cleaned to obtain a standard semi-structured dataset. Subsequently, based on this dataset, the optimization objectives (maximizing yield strength, maximizing low-temperature impact energy, and minimizing the weld crack sensitivity index), decision variables (chemical composition and process parameter data), and constraints (performance, element content range, process parameters, and corrosion resistance index constraints) are defined, and a multi-objective optimization model is constructed. Next, a mechanical performance prediction model integrating multiple performance parameters is trained using a machine learning algorithm. Finally, a reference vector-guided multi-objective optimization algorithm is used to iteratively calculate and obtain the optimal solution set. The final composition design scheme is then selected by weighting the target steel grade based on its service scenario. It can accurately quantify the complex mapping relationship between composition, process and performance, avoid the high cost of trial and error, and simultaneously optimize strength, toughness, weldability and corrosion resistance to match service requirements. Moreover, the optimization algorithm takes into account both global exploration and local development, efficiently obtains the optimal solution under multiple constraints, does not require manual experience derivation, has strong generalization ability, and can be extended to the composition design of other high-strength steels or special steels.

[0007] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0008] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This illustration shows a flowchart of a method for designing the composition of high-strength steel for ship plates based on multi-objective black-box optimization, as provided in an embodiment of this application. Figure 2 This illustration shows a flowchart of another method for designing the composition of high-strength steel for ship plates based on multi-objective black-box optimization, as provided in an embodiment of this application. Figure 3 This document illustrates a flowchart of a method for constructing a mechanical performance prediction model, as provided in an embodiment of this application. Figure 4 This paper presents a comparison chart of the actual and predicted values ​​of a yield strength prediction model for AH36 steel provided in an embodiment of this application. Figure 5 This illustration shows a schematic diagram of a multi-objective optimization algorithm provided in an embodiment of this application; Figure 6 This illustration shows a schematic diagram of an optimal solution decision-making and verification process provided in an embodiment of this application; Figure 7 A flowchart of a multi-objective composition optimization method for AH36 steel provided in an embodiment of this application is shown. Detailed Implementation

[0009] In the description of this application, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application.

[0010] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0011] Exemplary embodiments of the present application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this application will be thorough and complete, and will fully convey the scope of the present application to those skilled in the art.

[0012] High-strength low-alloy steels for shipbuilding (such as AH36) must meet multiple performance requirements during actual service, including low-temperature impact toughness, high weldability, and seawater corrosion resistance. Their material properties directly affect hull safety and service life. The performance of steel materials is determined by both chemical composition and manufacturing process, with chemical composition design being a crucial step. Current composition design mainly relies on three methods: empirical formulas (which struggle to reflect the interactions between components), experimental design (high cost, long cycle, and limited coverage), and computational simulation (lacking industrial-grade data support). Steel mills often combine these three methods, but it is difficult to efficiently balance the nonlinear coupling relationships between multiple indicators such as yield strength, impact toughness, and weldability, and it is impossible to quickly obtain the optimal composition combination that meets both specifications and requirements.

[0013] In recent years, black-box data analysis techniques, represented by machine learning, and multi-objective optimization techniques have played an increasingly important role in the field of materials design. Machine learning methods, by constructing a mapping relationship between material composition and properties, enable rapid prediction of steel material properties, effectively accelerating the material composition design process. Multi-objective optimization methods, on the other hand, use heuristic search strategies to quickly find the optimal combination of chemical compositions within a given search space. Current work has reported on the application of machine learning and multi-objective optimization techniques to guide the design of steel material compositions.

[0014] However, existing methods typically optimize for maximizing multiple mechanical properties of materials, failing to adequately consider the specific requirements of steel materials in downstream service scenarios. In practical applications, different service scenarios place significant differences in the performance emphasis of steel: for example, polar icebreakers emphasize extreme low-temperature impact toughness, ocean-going vessels need to balance high strength and corrosion resistance, while offshore engineering vessels focus more on the adaptability of welding processes. Furthermore, existing methods do not address the process constraints in material composition design, nor the implicit constraints existing in the synergistic relationships between components.

[0015] To address this issue, this application proposes a method for designing the chemical composition of high-strength ship plate steel using a multi-objective optimization strategy, with the overall service quality of the steel plate as the optimization objective. This method can synergistically optimize strength, toughness, and weldability, thereby obtaining a set of Pareto-optimal high-performance chemical composition design schemes that meet the requirements for ship steel use. The implementing entity of this application can be a multi-objective black-box optimization-based high-strength ship plate steel material composition design system, relying on the computing power of a server to provide services to users. The server can be a standalone server or a server providing basic cloud computing services such as cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, content delivery networks (CDN), and big data and artificial intelligence platforms.

[0016] This application provides a method for designing the composition of high-strength ship plate materials based on multi-objective black-box optimization, such as... Figure 1 As shown, the method includes: 101. Obtain historical data of high-strength steel materials for ship plates collected from the steel plant's production and manufacturing management system, perform data alignment and data cleaning on the historical data of high-strength steel materials for ship plates, and obtain a standard semi-structured dataset.

[0017] In this embodiment, the steel mill production management system is an information system that coordinates the entire steel mill production process, responsible for recording information on all aspects, including production planning and process execution. Historical data for high-strength steel materials used in shipbuilding plates includes product specification data, chemical composition data, process parameter data, and performance index data. Product specification data includes, but is not limited to, steel grade, plate width, plate thickness, and plate length. Chemical composition data includes, but is not limited to, the content of elements such as C, Mn, Si, Cr, Ni, Mo, V, Nb, Ti, Al, Cu, B, P, and S. Process parameter data includes, but is not limited to, key process parameters such as finishing rolling start temperature, initial cooling temperature, and final cooling temperature. Performance index data includes, but is not limited to, performance indicators such as yield strength, tensile strength, and low-temperature impact absorption energy (–20°C). The collected data is aligned into standardized semi-structured data in the order of product specification-chemical composition-key process parameters-mechanical properties. Data cleaning is then performed on the aligned semi-structured data, including missing value filling, outlier removal, and standardization. By performing alignment and cleaning, a standard semi-structured dataset is finally obtained, in which each record contains complete, consistent and reliable information, fundamentally ensuring the quality and consistency of the input data and eliminating the interference of noise and erroneous records on subsequent data-driven models.

[0018] 102. Based on the standard semi-structured dataset, determine the optimization objective, decision variables and constraints of the target steel grade, and construct a multi-objective optimization model for the target steel grade using the optimization objective, decision variables and constraints of the target steel grade.

[0019] In this embodiment, based on the actual performance requirements of high-strength ship plate steel in typical ship service scenarios, optimization targets are selected with the mechanical properties and weldability of the material as the core performance indicators. These optimization targets include maximizing yield strength to meet the load-bearing capacity requirements of the hull structure; maximizing low-temperature impact energy to ensure excellent toughness of the material in low-temperature environments; and minimizing the weld crack sensitivity index to optimize the weldability of the steel and reduce the tendency for weld cracking. Decision variables include chemical composition data and process parameter data, serving as the core inputs for performance control. The mass fraction (wt.%) of chemical elements that significantly affect the performance of the steel plate and are controllable during the smelting process are selected as decision variables, specifically including: C, Mn, Si, Cr, Ni, Mo, Cu, V, Nb, Ti, Al, and B. The content of each element is adjusted within a set upper and lower limit range, which is determined based on national standards (such as GB / T 712-2011) and historical production data from steel mills. Considering the critical impact of the rolling process on the mechanical properties of thick steel plates, key rolling process parameters are incorporated into the decision variables. These parameters include, but are not limited to, the initial rolling temperature, initial cooling temperature, and final cooling temperature. These parameters are limited to the adjustable range of the current production process. Constraints related to the service scenario are considered, including performance constraints, element content range constraints, process parameter constraints, and corrosion resistance index constraints. By mathematically formalizing and precisely expressing the comprehensive material requirements of the service scenario, complex engineering experience, national standards, and process knowledge are integrated into a clearly structured and well-defined optimization framework, providing a clear direction and feasibility judgment criteria for subsequent automated optimization.

[0020] 103. Using machine learning algorithms to train a standard semi-structured dataset, a mechanical property prediction model integrating yield strength prediction model, tensile strength prediction model and low temperature impact energy prediction model for the target steel grade is obtained.

[0021] In this application embodiment, a rapid and accurate mapping relationship from composition and process to key performance is established to replace high-cost physical experiments. The mechanical performance prediction model is an integrated model set containing three independent XGBoost regression models trained respectively for yield strength, tensile strength, and low-temperature impact energy. These models are used to accurately predict key performance indicators such as yield strength, low-temperature impact energy, and weldability under specific chemical compositions, serving as the fitness function in the optimization algorithm to improve design efficiency and accuracy.

[0022] 104. A multi-objective optimization algorithm guided by reference vectors is used to iteratively calculate the multi-objective optimization model and the mechanical performance prediction model to obtain the optimal solution set. Based on the service scenario of the target steel grade, weights are assigned, and the high-strength steel material composition design scheme of the target steel grade for ship plates is selected from the optimal solution set.

[0023] In this embodiment, a reference vector-guided multi-objective optimization framework is adopted, introducing a dual-channel individual generation strategy of fractal random walk and conditional diffusion model. This strategy maintains global diversity during the search process while efficiently utilizing historical excellent solutions, rapidly uncovering non-inferior chemical composition combinations that satisfy multiple performance constraints within a complex design space. The reference vector-guided multi-objective optimization algorithm is an advanced evolutionary algorithm that guides the search direction through a set of uniformly distributed reference vectors and uses angular penalty distance (APD) to balance the convergence and distribution of solutions. Weights are assigned based on the specific service scenario of the target ship, and the final solution is selected from the solution set. This approach efficiently and automatically searches for a batch of high-quality, diverse optimal solutions in a high-dimensional, complex constraint space, rather than a single solution.

[0024] This application provides a method for designing the composition of high-strength ship plate materials based on multi-objective black-box optimization. Compared with the prior art, this application collects historical data such as product specifications, chemical composition, process parameters, and performance indicators of high-strength ship plate materials from the steel plant's production and manufacturing management system. After alignment and cleaning, a standard semi-structured dataset is obtained. Then, based on this dataset, the optimization objectives (maximizing yield strength, maximizing low-temperature impact energy, and minimizing the weld crack sensitivity index), decision variables (chemical composition and process parameter data), and constraints (performance, element content range, process parameters, and corrosion resistance index constraints) are defined to construct a multi-objective optimization model. A mechanical performance prediction model integrating multiple performance parameters is then trained using a machine learning algorithm. Finally, a reference vector-guided multi-objective optimization algorithm is used to iteratively calculate and obtain the optimal solution set. The final composition design scheme is then selected by weighting the target steel grade based on the service scenario. It can accurately quantify the complex mapping relationship between composition, process and performance, avoid the high cost of trial and error, and simultaneously optimize strength, toughness, weldability and corrosion resistance to match service requirements. Moreover, the optimization algorithm takes into account both global exploration and local development, efficiently obtains the optimal solution under multiple constraints, does not require manual experience derivation, has strong generalization ability, and can be extended to the composition design of other high-strength steels or special steels.

[0025] Furthermore, as a refinement and extension of the specific implementation methods of the above embodiments, and in order to fully illustrate the specific implementation process of this embodiment, this application provides another method for designing the composition of high-strength steel materials for ship plates based on multi-objective black-box optimization, such as... Figure 2 As shown, the method includes: 201. Obtain historical data of high-strength steel materials for ship plates collected from the steel plant's production and manufacturing management system, perform data alignment and data cleaning on the historical data of high-strength steel materials for ship plates, and obtain a standard semi-structured dataset.

[0026] In this embodiment, historical data of high-strength steel for ship plates is aligned according to the order of product specifications, chemical composition, key process parameters, and mechanical properties to obtain semi-structured data. ,in, Let represent the i-th steel plate sample, and n represent the number of steel plate samples.

[0027] In the semi-structured data, at least one missing feature value is identified, and the missing rate of each missing feature value is calculated. Missing feature values ​​with a missing rate greater than or equal to a preset missing threshold are deleted from the semi-structured data, resulting in the deleted semi-structured data. The preset missing threshold can be 0.15%. Missing feature values ​​with a missing rate less than the preset missing threshold are selected from the at least one missing feature value to obtain at least one target missing feature value. The mean value of the same steel grade data corresponding to each target missing feature value is obtained. In the deleted semi-structured data, the mean value of the same steel grade data corresponding to each target missing feature value is used to fill in each target missing feature value, resulting in the semi-structured data after missing feature processing.

[0028] Multiple continuous feature fields were identified in the semi-structured data after missing data processing. For each continuous feature field, its mean and standard deviation were calculated, and based on the standard deviation criterion, the outlier identification interval for the continuous feature field was determined using its mean and standard deviation. ,in, This represents the mean. This represents the standard deviation. If any data point in the continuous feature field falls within the outlier detection range of the continuous feature field, then the continuous feature field will be removed from the semi-structured data after missing data processing.

[0029] By processing each continuous feature field in the semi-structured data after missing data processing in sequence, a standard semi-structured dataset can be obtained.

[0030] By systematically aligning historical production data, handling missing values ​​based on thresholds, and applying statistical methods... Outlier cleaning of the data (based on the criteria) constructs a high-quality, highly consistent standard dataset. This is not a simple data organization process, but a refined process that integrates domain knowledge (such as processing by steel grade) and statistical principles. It can effectively identify and eliminate unreliable noisy data while retaining valuable information to the maximum extent. This provides a solid and clean data foundation for subsequent machine learning modeling and optimization decisions, significantly improving the reliability of intelligent design of material composition.

[0031] 202. Based on the standard semi-structured dataset, determine the optimization objective, decision variables and constraints of the target steel grade, and construct a multi-objective optimization model for the target steel grade using the optimization objective, decision variables and constraints of the target steel grade.

[0032] In this embodiment, taking the actual application requirements of AH36 steel in a typical ship service environment as an example, optimization objectives, decision variables, and constraints are set. The specific process is as follows: Considering the service performance of AH36 marine steel in the marine environment, yield strength, low-temperature impact energy, and weld crack sensitivity index are selected as target variables, and the optimization objective is constructed as shown in Formula 1 below: Formula 1:

[0033] in, The objective function represents the yield strength, and the optimization objective is to maximize the yield strength to meet the load-bearing capacity requirements of the hull structure. The objective function represents the low-temperature impact energy, and the optimization objective is to maximize the low-temperature impact energy to ensure that the material has good toughness in low-temperature environments. This represents the weld crack sensitivity index. The optimization objective is to minimize this index, thereby optimizing the weldability of the steel and reducing the tendency for weld cracking. Specifically, for the aforementioned optimization objectives of yield strength and low-temperature impact energy, a precise quantification objective function is required. and The specific form of the mathematical function used to calculate and optimize this performance index is unknown. A mechanical performance prediction model will be built based on historical material composition-performance data using fitting modeling techniques. For The candidate chemical compositions were evaluated using the cold cracking sensitivity index recommended by the International Institute of Welding (IIW), and the calculation formula is shown in Formula 2 below: Formula 2:

[0034] Wherein, Pcm represents the cold cracking sensitivity index, and C, Mn, Si, Cr, Ni, Mo, Cu, V, and B represent chemical elements.

[0035] As the core input for performance control of medium and heavy steel plates, the chemical composition content of the steel and key process parameters during rolling are selected as decision variables for the optimization problem. Specifically, the mass fraction (wt.%) of chemical elements that significantly affect the performance of AH36 steel plates and are controllable during the smelting process are selected as decision variables, including C, Mn, Si, Cr, Ni, Mo, Cu, V, Nb, Ti, Al, etc. At the same time, considering the influence of the rolling process on the mechanical properties of medium and heavy steel plates, the main rolling process parameters are included in the decision variables, including but not limited to the finishing rolling start temperature, the start cooling temperature, and the final cooling temperature.

[0036] To address the practical application requirements of AH36 steel in typical marine service environments, a series of constraints were set during the optimization process to ensure the feasibility and reliability of the designed chemical composition scheme in engineering practice. Specifically: Define performance constraints. All performance indicators (including yield strength, tensile strength, and low-temperature impact energy, etc.) must meet the minimum requirements of the following national standard (GB / T 712-2011), as shown in Formula 3 below: Formula 3:

[0037] Where YS represents yield strength, TS represents tensile strength, and AKV represents low-temperature impact energy.

[0038] Determine the constraints on element content ranges. The content of each alloying element must fluctuate within the range specified in the national standard (GB / T 712-2011) to avoid excessive smelting difficulty or the formation of harmful structures. Further combining the steel plant's existing historical production data and internal composition control standards, the upper and lower limits are given in the following formula 4, according to the elemental order [C, Si, Mn, P, S, Cr, Ni, Cu, Mo, V, Al, Ti, Nb]. Formula 4:

[0039] Where upper represents the upper limit and lower represents the lower limit.

[0040] Determine process parameter constraints. For the rolling process of medium and heavy plates, the controllable key process nodes are the finishing rolling temperature and cooling rate of the steel plate. To ensure that the designed scheme can be implemented on the existing production line, based on the existing historical production data of the steel plant, the upper and lower limits of the three key process parameters—finishing rolling start temperature, starting cooling temperature, and final cooling temperature—are given in sequence as shown in Formula 5 below: Formula 5:

[0041] Determine corrosion index constraints. To ensure that the optimized chemical composition of AH36 steel exhibits good corrosion resistance in marine atmospheric environments, the ranges of key elements such as Cr, Cu, and Ni, as well as the upper limits of impurity elements P and S, must be constrained according to the quantitative relationship between alloy element content and CRI index in GB / T 41756-2022 standard. The Legault-Leckie equation given in GB / T 41756-2022 standard is based on industrial atmospheric corrosion data; however, for marine and semi-rural climates, the ranking of corrosion resistance indices for different steel compositions is the same. The Legault-Leckie equation is shown in Formula 6 below: Formula 6:

[0042] Where %Cu represents the mass fraction of Cu in the chemical composition, and the mass fractions of other chemical components are expressed in the same way. Therefore, the CRI index is calculated based on historical data from steel mills, and the average value of the CRI index calculated from historical data of AH36 steel is selected as the corrosion resistance index constraint as shown in Formula 7 below: Formula 7:

[0043] The final result is shown in Formula 8 below: Formula 8:

[0044]

[0045] Where x represents a vector consisting of all decision variables, This represents a vector containing the content of all chemical components.

[0046] By constructing a data-driven, service-oriented, and precise mathematical optimization framework, the optimization objectives, adjustable variables, and process boundaries of the target steel grade (such as AH36) are automatically extracted from cleaned standard historical data. This transforms complex engineering experience, national standards, and production constraints into a structured mathematical model. This transforms the engineering problem of designing high-performance ship plate steel from an experience-based qualitative exploration into a quantifiable and computable scientific optimization problem, greatly improving the design's relevance, systematic approach, and efficiency.

[0047] To establish a set of mechanical property prediction models for multi-objective optimization solutions, and to accurately predict key performance indicators such as yield strength and low-temperature impact energy under specific chemical compositions, these models will serve as fitness functions in the optimization algorithm, thereby improving design efficiency and accuracy. The flowchart for constructing the mechanical property prediction model is as follows: Figure 3As shown, the steps include: first, based on historical data, the target thickness is screened to lock in the product specifications; then, similar steel grade data is clustered and merged to enhance the sample; feature selection and data segmentation are performed to clarify the input and the dataset; then, a high-precision prediction model is obtained through model training and validation; finally, a unified prediction service is formed through model integration and deployment. The specific steps are as follows: 203-205.

[0048] 203. The standard semi-structured dataset is processed using the K-means clustering algorithm to obtain the main dataset and the auxiliary dataset.

[0049] In this embodiment, the selection criteria for steel material thickness are determined based on the application scenario of the target steel grade, and a sample dataset that meets the selection criteria for steel material thickness is selected from the standard semi-structured dataset. , This represents the i-th steel plate sample. This indicates the number of steel plate samples selected after screening. Since this application primarily targets medium-thick steel plates used in main decks, side platings, bottom platings, strong frames, and important bulkheads, whose characteristic thickness range is generally 20mm to 40mm, based on this thickness condition, medium-thick plate data with a thickness of 20mm-40mm from historical production data were selected as the sample dataset.

[0050] Obtain a subset of steel grade numbers, including multiple steel grades such as AH36, DH36, and EH36. Calculate the multi-dimensional mean of the sample dataset according to the steel grade number subset, generating a mean vector for each steel grade number, as shown in Formula 9 below: Formula 9:

[0051] in, Let represent the mean vector of the j-th steel grade. This represents the arithmetic mean of the j-th steel grade on the k-th attribute. denoted by , where p represents the number of steel grades, and p represents the dimension of the mean vector.

[0052] The K-means clustering algorithm is used to perform unsupervised clustering on the mean vectors of multiple steel grades, grouping similar steel grades into the same material category, obtaining multiple clustering results, and selecting the clustering result corresponding to the target steel grade from the multiple clustering results as the target clustering result.

[0053] The data corresponding to the target steel grade (AH36) in the target clustering results is used as the main dataset. The data in the target clustering results, excluding the data corresponding to the target steel grade, i.e., the historical data of other steel grades (such as DH36, EH36, etc.) belonging to the same category as AH36 steel, are used as auxiliary datasets. , This indicates the number of samples in the main dataset. This indicates the number of samples in the auxiliary dataset.

[0054] By employing the K-means clustering algorithm to intelligently categorize historical data across multiple steel grades, a precise balance between targeted learning and enhanced generalization is achieved. Specifically, target scenario data is identified based on product specifications (20-40mm thickness) to ensure targeted learning. Then, by calculating the mean feature vectors of each steel grade and performing clustering, the cluster of steel grades (such as DH36 and EH36) most closely related to the target steel grade (AH36) in terms of process and composition characteristics are automatically identified from the perspective of data similarity (rather than subjective experience). Data from these clustered steel grades is transformed into a high-quality auxiliary training set, effectively expanding the scale and diversity of the training samples without introducing irrelevant noise. Its direct advantage is a significant enhancement of the generalization ability and robustness of subsequent mechanical property prediction models, enabling them to more accurately depict the complex mapping relationship between composition, process, and performance, thereby overcoming the defect of overfitting that may result from limited data for a single grade.

[0055] 204. Divide the main dataset into a training subset and a test subset according to a preset ratio. Use the training subset and the auxiliary dataset as the training set. Use the chemical composition data and process parameter data in the training set as input features and the performance index data in the training set as output labels.

[0056] In this embodiment, since the feature combination mechanism of the tree structure model can effectively capture the complex interaction between chemical composition and mechanical properties, a regression prediction model based on a gradient decision tree framework (such as the XGboost algorithm) is chosen for model training. First, the main dataset is divided into training subsets according to a preset ratio (preferably 7:3). and test subset ,in, This indicates the number of samples in the training subset. This indicates the number of samples in the test subset.

[0057] Use the training subset and auxiliary dataset as the training set. , This indicates the number of samples in the training set. Considering the limited amount of actual AH36 steel data, using clustered data of steel grades belonging to the same category as AH36 steel as an auxiliary dataset can improve the model's generalization ability and avoid overfitting.

[0058] The chemical composition data and process parameter data in the training set, i.e., decision variables (including but not limited to the content of elements such as C, Mn, Si, P, S, Cr, Ni, Mo, Cu, V, Nb, Ti, Al, and B, and key process parameters such as finishing rolling start temperature, starting cooling temperature, final cooling temperature, and cooling rate), are used as input features. Where m is the feature dimension, and the performance metrics data in the training set are used as the output labels. The output labels include yield strength, tensile strength, and low-temperature impact energy.

[0059] This paper effectively addresses the fundamental challenge of limited historical data for specific materials (such as AH36 steel) in industrial scenarios by employing a structured data augmentation and validation mechanism. Specifically, the main data is first divided in a 7:3 ratio to ensure the fairness of model evaluation. Crucially, the paper creatively integrates clustered auxiliary data of the same category with the main training subset. This essentially uses similar steel grades to fill the gap in data for the target steel grade, significantly expanding the composition-process-performance relationship spectrum learned by the model. This significantly improves the generalization ability and robustness of machine learning models (especially algorithms like XGBoost that can capture complex interactions), making them more accurate in predicting new formulations while fundamentally avoiding overfitting problems that are prone to occur due to data scarcity.

[0060] 205. Using input features and output labels, the XGBoost model is trained to obtain the mechanical property prediction model of the target steel grade, which integrates the yield strength prediction model, tensile strength prediction model and low temperature impact energy prediction model.

[0061] In this embodiment, the XGBoost model is trained using input features and output labels to obtain the yield strength prediction model, tensile strength prediction model, and low-temperature impact energy prediction model for the target steel grade, as shown in the following formula 10: Formula 10:

[0062]

[0063]

[0064] in, This represents the yield strength prediction model. This represents a tensile strength prediction model. This represents a low-temperature impact energy prediction model. Indicates input features, This indicates the yield strength label data in the output labels. This represents the measured yield strength value corresponding to the i-th training sample in the training set. This indicates the tensile strength label data in the output label. This represents the measured tensile strength value corresponding to the i-th training sample in the training set. This indicates the low-temperature impact energy tag data in the output tag. This represents the measured value of the low-temperature impact energy corresponding to the i-th training sample in the training set. All three models use the XGBoost algorithm and have the same training set. However, for the yield strength prediction model, the input is the decision variable, and the output is only the yield strength; for the tensile strength prediction model, the input is the decision variable, and the output is only the tensile strength, and so on. In other words, a separate model is trained for each label.

[0065] The yield strength prediction model, tensile strength prediction model and low temperature impact energy prediction model of the target steel grade are integrated into a mechanical property prediction model of the target steel grade. It can receive the same chemical composition and process parameter input vector and output the predicted values ​​of multiple key performance indicators simultaneously.

[0066] The integrated mechanical property prediction model set is then deployed into a multi-objective optimization algorithm. During the optimization algorithm iteration process, the deployed model set serves as the core fitness function calculation module, receiving candidate chemical composition-process schemes in real time, predicting their corresponding yield strength, tensile strength, and low-temperature impact energy, and feeding these predicted values ​​back to the optimization algorithm to evaluate the merits of the schemes and guide subsequent search directions.

[0067] Optionally, the performance of the yield strength prediction model, tensile strength prediction model and low temperature impact energy prediction model are evaluated by using a test subset, respectively, to obtain the key evaluation indicators corresponding to the yield strength prediction model, the tensile strength prediction model and the low temperature impact energy prediction model. The key evaluation indicators include root mean square error, mean absolute error and coefficient of determination. If the key evaluation indicators corresponding to the yield strength prediction model do not meet the key evaluation indicator verification conditions, and / or the key evaluation indicators corresponding to the tensile strength prediction model and / or the key evaluation indicators corresponding to the low-temperature impact energy prediction model do not meet the key evaluation indicator verification conditions, then the XGBoost model will be retrained using the input features and output labels. The key evaluation indicator verification conditions include root mean square error less than or equal to the root mean square error threshold, mean absolute error less than or equal to the mean absolute error, and coefficient of determination greater than or equal to the coefficient of determination threshold. Taking yield strength as an example, the comparison between the model's predicted and actual yield strength values ​​for the test subset is shown in the figure below. Figure 4 As shown, the solid line representing the measured value and the dashed line representing the model prediction value closely follow each other in most sample intervals, and the overall trend is highly consistent. This indicates that the constructed XGBoost prediction model can effectively learn and reproduce the complex law of yield strength variation with composition and process, and has good overall fitting ability.

[0068] This application employs a reference vector-guided multi-objective optimization framework, introducing a dual-channel individual generation strategy of fractal random walk and conditional diffusion generation. This strategy maintains global diversity while efficiently utilizing historical best solutions, enabling the rapid discovery of non-inferior chemical composition combinations that satisfy multiple performance constraints within a complex design space. The flowchart of this multi-objective optimization algorithm is shown below. Figure 5 As shown, the steps include: starting with initializing the population and reference vector, followed by evaluating the fitness of the population; the process executes two core offspring generation strategies in parallel: one is a fractal random walk combining Gaussian and Levy perturbations, and the other is a conditional diffusion model based on APD conditional sampling; after all generated offspring are evaluated, they enter the environment selection stage together with their parents to select elite individuals to form the new generation of the population, and update the reference vector to guide the search direction; this process iteratively judges whether the termination condition has been met, if not, it continues to iterate, if so, the final population is output as the optimal solution set and the process ends, the specific implementation steps are as follows 206-216.

[0069] 206. The initial population is generated in the decision variable space of the multi-objective optimization model using the Latin hypercube sampling method, and the Denniss method is used to generate a uniformly distributed set of reference vectors in the objective variable space of the multi-objective optimization model.

[0070] In this embodiment, the population size, maximum number of iterations, maximum number of evaluations, proportion of individuals undergoing fractal random walks, and proportion of individuals generated through diffusion-guided generation are set. The maximum number of iterations is determined based on the maximum number of evaluations. The current number of evaluations refers to the calculation of an individual's fitness vector during the evolutionary process, which is considered one evaluation. For example, when the initial population size is 100 (i.e., containing 100 individuals), the fitness function needs to be called to evaluate the quality of these 100 individuals, and the current number of evaluations is 100. After entering the evolutionary stage, each generation must evaluate the newly generated individuals and accumulate the number of evaluations. When the accumulated number reaches the maximum number of evaluations, the algorithm stops running.

[0071] The Latin Hypercube Sampling (LHS) method is used to generate an initial population in the decision variable space of a multi-objective optimization model. ,in, Let represent the i-th individual, and N represent the population size. Each individual represents a design scheme for the composition of high-strength steel for ship plates of a target steel grade. This design scheme includes the composition values ​​of each chemical component, the parameters for the initial rolling temperature, the initial cooling temperature, and the final cooling temperature. It is important to note that to ensure the initial population meets the physical meaning and constraints, if an individual does not meet the constraints of the multi-objective optimization model, random resampling is used until the number of individuals meeting the constraints reaches the population size.

[0072] The Denniss method is used to generate a uniformly distributed set of reference vectors in the objective variable space of a multi-objective optimization model. ,in, This represents the Kth reference vector. Each reference vector has a dimension of 3, and the value of K is generally equal to N.

[0073] The Latin hypercube sampling method ensures that the initial population uniformly covers the entire feasible region within the high-dimensional decision space composed of chemical composition and process parameters, avoiding the uneven distribution that may result from random sampling, and giving the algorithm the potential for comprehensive exploration from the outset. Meanwhile, the Dennis method generates uniformly distributed reference vectors, pre-setting clear and dispersed guiding directions for multi-objective search. The combination of these two methods not only guarantees the diversity and quality of the initial population, but its mechanism of resampling if constraints are not met also ensures that all starting points are engineering-feasible. This effectively helps the algorithm escape local optima and accelerates convergence towards the true Pareto front.

[0074] 207. For the current iteration number, call the mechanical performance prediction model to calculate the predicted yield strength, tensile strength and low temperature impact energy of each individual in the current population, calculate the welding crack sensitivity index of each individual, and use the predicted yield strength, low temperature impact energy and welding crack sensitivity index of each individual to form the fitness vector of each individual.

[0075] In this embodiment, for the current iteration number, the mechanical property prediction model is invoked to calculate the predicted yield strength, tensile strength, and low-temperature impact energy of each individual in the current population. The welding crack sensitivity index of each individual is also calculated. The predicted yield strength, low-temperature impact energy, and welding crack sensitivity index of each individual are then used to construct the fitness vector of that individual. , This represents the predicted yield strength value of the i-th individual at the current iteration number t. This represents the predicted value of the cryogenic shock energy for the i-th individual at the current iteration number t. Let represent the welding crack sensitivity index of the i-th individual at the current iteration number t. The predicted tensile strength value of each individual meets the constraints of the multi-objective optimization model. Since the national standard has requirements for the tensile strength of AH36 steel, it is necessary to determine whether the generated new steel grade meets the national standard, that is, the predicted tensile strength value of the individual needs to meet the constraints of the multi-objective optimization model.

[0076] 208. Calculate the set of APD values ​​for each individual based on the positional relationship between the fitness vector of each individual and the set of reference vectors.

[0077] In this embodiment, the fitness vector of each individual is normalized to obtain the target vector of each individual, as shown in Formula 11 below: Formula 11:

[0078] in, Let represent the target vector of the i-th individual at the current iteration number t. This represents the fitness vector of the i-th individual at the current iteration number t. This represents the vector formed by selecting the minimum value from the fitness vectors of each individual at the current iteration number t.

[0079] The angle values ​​between different reference vectors are calculated using a set of reference vectors, as shown in Formula 12 below: Formula 12:

[0080] in, This represents the angle between the i-th reference vector and the j-th reference vector. This represents the i-th reference vector in the set of reference vectors at the current iteration number t. This represents the j-th reference vector in the reference vector set at the current iteration number t.

[0081] For each reference vector, extract multiple angle values ​​between the reference vector and other reference vectors from the angle values ​​between different reference vectors. Select the angle value with the smallest value from the multiple angle values ​​as the target angle value of the reference vector. The other reference vectors are multiple reference vectors in the reference vector set other than the reference vector.

[0082] Calculate the angle between the target vector of each individual and multiple reference vectors, as shown in Formula 13 below: Formula 13:

[0083] in, This represents the angle between the i-th individual and the j-th reference vector. Let represent the target vector of the i-th individual at the current iteration number t. This represents the j-th reference vector in the reference vector set at the current iteration number t.

[0084] The APD value between each individual and multiple reference vectors is calculated using the angle between each individual's target vector and multiple reference vectors, the target angle value of each reference vector, and the target vector of each individual, as shown in Formula 14 below: Formula 14:

[0085] in, Let represent the APD (angle-penalized distance) value between the i-th individual and the j-th reference vector. The APD value, as a comprehensive metric, can simultaneously evaluate the convergence and diversity of candidate solutions, guiding the population towards a uniform distribution towards the Pareto front. 3 represents the number of optimization objectives, and t represents the current iteration number. This represents the maximum number of iterations. In multi-objective optimization algorithms, it is generally calculated by dividing the maximum number of evaluations by the population size N. It is determined by the maximum number of evaluations, and the maximum number of iterations is guaranteed to be an integer when setting the parameters. This represents the angle between the i-th individual and the j-th reference vector. Let represent the target vector of the i-th individual at the current iteration number t. This represents the target angle value of the j-th reference vector. This represents a user-defined coefficient, typically 2. N represents the population size, and K represents the number of reference vectors.

[0086] The APD values ​​between each individual and multiple reference vectors are used as the set of APD values ​​for each individual.

[0087] This paper uses mathematical formulas to quantify, unify, and dynamically balance the two competing objectives of convergence and diversity in multi-objective optimization. Specifically, the APD value is determined by the convergence term. and distribution penalty term Together they constitute, and are weighted by a factor that increases over time. Achieving adaptive adjustment: In the early stages of evolution, emphasis is placed on convergence to quickly approach the frontier, while in the later stages, distribution penalties are strengthened to obtain a uniformly distributed solution set. This mechanism can intelligently guide the population to systematically search and ultimately output a high-quality, highly diverse set of Pareto optimal solutions in a complex performance trade-off space (such as strength, toughness, and weldability). This provides rich and balanced optimal solutions for materials design, fundamentally overcoming the shortcomings of traditional optimization methods that are prone to getting trapped in local optima or unevenly distributed solution sets.

[0088] 209. A dual-channel strategy of fractal random walk and conditional diffusion model is adopted to generate offspring population based on the set of APD values ​​of each individual.

[0089] In this embodiment of the application, for each individual, the APD value with the smallest value is selected from the individual's APD value set as the individual's target APD value, as shown in the following formula 15: Formula 15:

[0090] in, This represents the target APD value for the i-th individual. Let N represent the APD value between the i-th individual and the j-th reference vector, and let N represent the population size.

[0091] Population size and the proportion of fractal random walk individuals The product of is used as the first quantity.

[0092] Sort the individuals in the current population in descending order of their target APD values. Starting from the first individual in the sorting results, select the first number of individuals as the parent individuals for the fractal random walk. Apply fractal motion to perturb the fractal dimension of each parent individual to obtain the first number of offspring individuals generated by the fractal random walk, as shown in Formula 16 below: Formula 16:

[0093] in, This represents the i-th offspring generated by the fractal random walk in the next iteration t+1. This represents the i-th parent individual in the current iteration t. This represents a dimensional mask vector of length m, used to indicate which dimensions are involved in the update. This represents the Hadamard product operator. The scaling factor of the Levy distribution. This represents the index that controls the Levy distribution. The scaling factor representing the Gaussian distribution. For the parameters of the Gaussian distribution, Indicates the optimal parent individual position. It represents the standard deviation.

[0094] Population size and the proportion of individuals generated by diffusion-guided generation The product of is used as the second quantity.

[0095] Data vector of each individual The target APD value of each individual is combined to obtain the extended vector of each individual, as shown in Formula 17 below: Formula 17:

[0096] in, This represents the expansion vector of the i-th individual at the current iteration number t. This represents the data vector of the i-th individual at the current iteration number t. Let m represent the target APD value of the i-th individual at the current iteration number t, and m represent the dimension of the decision variable.

[0097] The extended vector of each individual is input into the Conditional Diffusion Model (CDM) to guide the generation of individuals with smaller APD values, resulting in a second number of offspring individuals generated by the Conditional Diffusion Model, as shown in Formula 18 below: Formula 18:

[0098] in, This represents the i-th offspring generated by the conditional diffusion model in the next iteration t+1. Represents the extended vector set, Let N represent the expansion vector of the i-th individual at the current iteration number t, and let N represent the population size.

[0099] The first number of offspring individuals generated by fractal random walk and the second number of offspring individuals generated by conditional diffusion model are used as the offspring population.

[0100] The dual-channel offspring generation strategy, combining fractal random walks and conditional diffusion models, achieves intelligent complementarity and dynamic balance between exploration and guidance, significantly improving the search efficiency and solution quality of optimization algorithms in complex high-dimensional spaces. Specifically, fractal random walks selectively perturb some decision variables through dimensionality masks and combine this with random switching between Levy flight (large-scale exploration) and Gaussian perturbation (local exploitation) to effectively maintain population diversity and enhance the algorithm's ability to escape local optima. The innovation of the conditional diffusion model lies in binding an individual's feature vector to its performance evaluation index (target APD value) as a condition. Through a denoising diffusion process, it learns the distribution patterns of high-quality solutions, thereby directly and intelligently generating new individuals with better performance (smaller APD values). This combination enables the algorithm to conduct both extensive and diverse random exploration and targeted generation with clear objectives, synergistically driving the population to converge rapidly and stably to the global Pareto front and discovering high-quality trade-off solutions that are difficult for traditional evolutionary operators to reach.

[0101] 210. Use the mechanical property prediction model to calculate the predicted yield strength, tensile strength, and low-temperature impact energy of each offspring individual in the offspring population. Calculate the welding crack sensitivity index of each offspring individual. Use the predicted yield strength, low-temperature impact energy, and welding crack sensitivity index of each offspring individual to form the fitness vector of each offspring individual. Use the constraints of the multi-objective optimization model to test the fitness vector and tensile strength prediction of each offspring individual. If the test passes, proceed to step 211 below; if the test fails, proceed to step 212 below.

[0102] In this embodiment, a mechanical performance prediction model is invoked to predict the mechanical performance parameters of each offspring individual in the offspring population. Specifically, this includes calculating the predicted yield strength, tensile strength, and low-temperature impact energy based on material composition and process conditions. Subsequently, the welding crack sensitivity index of each offspring individual is further calculated according to Formula 2. This index is used to evaluate the crack resistance of the material during the welding process. Using the predicted yield strength, low-temperature impact energy, and welding crack sensitivity index of each offspring individual, a multi-dimensional fitness vector is constructed to comprehensively evaluate its overall performance. Furthermore, the pre-set constraints in the multi-objective optimization model are used to perform feasibility testing and constraint judgment on the fitness vector and its predicted tensile strength of each offspring individual. If the test passes, step 211 is executed; if the test fails, step 212 is executed.

[0103] 211. If the detection passes, the current population and the offspring population are combined into a merged population. The RVEA algorithm is used to select multiple new individuals from the merged population as the next generation population.

[0104] In this embodiment of the application, the APD value between each new individual and multiple reference vectors is calculated using formulas 11-14 based on the positional relationship between the fitness vector of each new individual in the merged population and the set of reference vectors.

[0105] For each reference vector, determine the APD value between each new individual and the reference vector, and select the new individual with the smallest APD value as the target individual. Based on the APD values ​​between each new individual and multiple reference vectors, process each reference vector separately to obtain multiple target individuals, and use these multiple target individuals as the initial parent population.

[0106] For example, given K reference vectors, for each reference vector, we need to select the individual with the smallest APD distance from all individuals in the merged population as the representative solution for that reference vector. Typically, K=N is set so that when the individuals selected for each reference vector are all unique, the population size reaches the set N. However, in reality, there might be cases where the representative solution for two reference vectors is the same individual, resulting in duplicate individuals. In this case, the number of individuals in the population will be less than the set N.

[0107] Therefore, the number of individuals in the initial parent population is counted. When the number of individuals in the initial parent population is less than the population size, the new individuals with the smallest APD value are selected from the other new individuals and added to the initial parent population. This process continues until the number of individuals in the initial parent population after addition equals the population size, thus obtaining the next generation population. Here, the other new individuals are multiple new individuals in the merged population, excluding the multiple target individuals. When the number of individuals in the initial parent population equals the population size, the initial parent population is used as the next generation population.

[0108] This environmental selection mechanism, through a two-stage elite selection strategy guided by reference vectors, achieves a precise balance and efficient maintenance of convergence and distribution in multi-objective optimization. Specifically, the algorithm first selects a representative solution from the merged population that best fits that direction (i.e., has the smallest APD value) for each preset reference vector direction (representing an ideal trade-off point on the Pareto front). This fundamentally ensures that the next generation of the population can be widely and evenly distributed across various potential optimal trade-off directions in the target space. When multiple reference vectors select the same representative solution, resulting in insufficient population size, the algorithm enters the second stage, automatically supplementing from the remaining high-quality individuals that were not selected, ensuring the stability of the population size and the excellent overall quality. This mechanism not only efficiently avoids the problems of uneven distribution or clustering of solution sets in traditional methods, but also ensures that elite individuals possess excellent convergence through a comprehensive consideration of APD values ​​(including both distance and angle penalties), thereby systematically driving the entire population to robustly evolve towards a high-quality, high-coverage Pareto optimal front.

[0109] 212. If the test fails, identify the offspring individuals that failed the test, delete the offspring individuals that failed the test, determine the generation strategy corresponding to the offspring individuals that failed the test, and regenerate the offspring individuals using the generation strategy.

[0110] In this embodiment, if the detection result fails, the system first identifies the specific offspring individuals that failed the detection and immediately removes these individuals from the current population. Then, it analyzes and determines the generation strategy that caused these individuals to fail the detection; this strategy is either a fractal random walk or a conditional diffusion model. Based on the determined generation strategy, it regenerates offspring individuals that meet the conditions to replace the previously deleted invalid solutions. This method does not simply discard invalid solutions but adaptively performs repair operations according to the strategy, thereby ensuring that every individual in the population is a feasible solution that satisfies the constraints. This mechanism not only helps maintain the overall quality of the population and ensures the effectiveness and consistency of the evolutionary direction but also effectively avoids the additional computational overhead caused by the continuous accumulation of invalid individuals. In this way, the optimization algorithm achieves significant improvements in both convergence speed and the practical engineering feasibility of the solution, making the entire process more efficient and reliable.

[0111] 213. Update the reference vector set for the current iteration number to obtain the reference vector set for the next iteration number.

[0112] In this embodiment, the reference vector set for the current iteration number is updated to obtain the reference vector set for the next iteration number, as shown in Formula 19 below: Formula 19:

[0113] in, This represents the i-th reference vector in the set of reference vectors for the next iteration number t+1. This represents the i-th reference vector in the reference vector set for the current iteration number t. This represents the Hadamard product operator. This represents the vector formed by selecting the maximum value from the fitness vectors of each individual at the current iteration number t. This represents the vector formed by selecting the minimum value from the fitness vectors of each individual at the current iteration number t. and It is renewed in each generation along with the current population.

[0114] 214. Count the number of fitness function evaluations. If the number of fitness function evaluations is less than the maximum number of evaluations, proceed to step 215 below; if the number of fitness function evaluations is equal to the maximum number of evaluations, proceed to step 216 below.

[0115] In this embodiment, the number of fitness function evaluations is counted. If the number of fitness function evaluations is less than the maximum number of evaluations, step 215 is executed; if the number of fitness function evaluations is equal to the maximum number of evaluations, step 216 is executed. This process design fully ensures that the optimization search process can be carried out effectively and efficiently within the allocated computing resources, while also strictly preventing resource waste caused by infinite loops or excessive iterations. This ensures that the entire optimization process is controllable, the results are predictable, and the experiments are reproducible under the same conditions.

[0116] 215. If the number of fitness function evaluations is less than the maximum number of evaluations, then the next generation population and the reference vector set for the next iteration are used to enter the next round of iteration calculation.

[0117] In the embodiments of this application, if the number of fitness function evaluations is less than the maximum number of evaluations, the next generation population and the reference vector set of the next iteration number are used to enter the next round of iteration calculation, driving the population to continuously evolve towards a better and more uniform Pareto front. Its advantage is that a delicate balance between search depth and computational cost is achieved through quantitative budgeting, ensuring that the algorithm achieves full convergence within limited resources.

[0118] 216. If the number of evaluations of the fitness function is equal to the maximum number of evaluations, then the next generation of the population is taken as the optimal solution set.

[0119] In the embodiments of this application, if the number of fitness function evaluations is equal to the maximum number of evaluations, then the next generation population is taken as the optimal solution set, wherein each individual in the optimal solution set represents a composition design scheme for a target steel grade.

[0120] 217. Based on the service scenarios of the target steel grade, assign weights and select the high-strength steel material composition design scheme of the target steel grade in the optimal solution set.

[0121] In this embodiment, based on the performance preferences of the target service scenario, target weights are assigned according to the type of ship components, and a weighted method is used to select the final solution from the optimal solution set. For example, given the target weights... ,in Multiple objective values ​​in the optimal solution set can be transformed into a single objective value according to their weights, as shown in Formula 20 below: Formula 20:

[0122] target value The smallest individual is considered the optimal solution. For each optimal solution, the final solution assigns a fixed value to each element. However, in actual steel production, the composition ratio of steel materials is usually difficult to control precisely at this fixed value. Therefore, a range with smaller fluctuations and easier implementation is generally set based on the fixed value of the optimal solution.

[0123] Optionally, the selected scheme can be subjected to smelting feasibility verification to ensure compliance with steel mill production line constraints; small-scale pilot furnace experiments can be conducted, and if the measured performance deviates from the predicted value... If so, then it is confirmed as the final design scheme; if there is a deviation... The experimental data is then fed back to the mechanical property prediction model for retraining, and the optimization process is restarted. Finally, executable component-process control parameters are output to the production system to form the final component design scheme.

[0124] The flowchart of the optimal solution decision-making and verification process is as follows: Figure 6As shown, a solution is selected from the Pareto optimal solution set obtained through multi-objective optimization. Then, rigorous process feasibility verification and small-scale experiments are performed sequentially for physical validation. Afterwards, the experimental results are evaluated through test analysis: if performance meets the standards, a process card is directly output for production and the process ends; if performance fails to meet the standards, re-optimization is triggered, and the experimental data is fed back to the model for improved predictions, subsequently re-entering the test analysis phase. By constructing a complete closed loop of "optimization-experiment-feedback," not only is the practical feasibility of the theoretical solution ensured through small-scale experiments, but more importantly, the experimental data is used as feedback signals to drive the continuous learning and optimization iteration of the model. This allows the design solution to continuously approach and ultimately meet all stringent engineering requirements in multiple iterations, achieving a robust transition from intelligent design to reliable production.

[0125] This application proposes a highly efficient multi-objective composition design method based on massive production data and intelligent algorithms. It effectively integrates service scenario requirements, national standards, and production process constraints to construct an accurate performance prediction model. Furthermore, it utilizes advanced multi-objective evolutionary algorithms to achieve intelligent optimization design of steel plate composition, driving the development of high-performance marine steel plates towards higher quality, higher reliability, and personalized customization. Crucially, by incorporating service scenarios into the material design process and constructing a "demand-oriented" design model, it not only achieves a shift from maximizing material performance to performance synergy and resource optimization but also promotes the precise definition of objective functions and constraints in optimization algorithms, improving the efficiency and accuracy of multi-objective optimization and ultimately achieving synergistic optimization of material design, performance prediction, and manufacturing processes. Compared with existing technologies, this application has the following advantages: First, it can accurately quantify the complex mapping relationship between composition, process, and performance, avoiding high-cost experiments that rely on trial and error based on experience; Second, it can simultaneously optimize strength, toughness, weldability, and corrosion resistance to meet the actual needs of downstream service scenarios for AH36 steel; Third, the proposed multi-objective evolutionary optimization algorithm can take into account both global exploration and local development, efficiently obtaining Pareto optimal solutions that satisfy multiple constraints; Fourth, based on data-driven and intelligent optimization algorithms, it does not require manual experience derivation, has good generalization ability, and can be extended to the composition design problems of other high-strength steel or special steel materials.

[0126] For example, based on the historical production data of a steel mill for 2024-2025, combined with national standards and the steel mill's experience, the composition optimization design method for high-strength ship plate materials based on multi-objective black-box optimization proposed in this application is applied for composition optimization design. Figure 7The flowchart of the multi-objective composition optimization method for AH36 steel is shown. Data acquisition and preprocessing lay a high-quality data foundation for the entire process. Multi-objective optimization problem modeling transforms service requirements into calculable mathematical objectives and constraints. Simultaneously, the mechanical performance prediction model is built using machine learning to rapidly predict from composition and process to performance. Both are input into the multi-objective optimization algorithm design stage, driving the algorithm to automatically search within the feasible region. Finally, through optimal solution screening and verification, the final composition-process solution that is both engineering-feasible and has the best performance is selected from a massive number of solutions. The performance of the mechanical performance model built based on historical data on the test set is shown in Table 1. Table 1: Performance metrics of the XGBoost model on the pre-defined test set

[0127] As shown in Table 1, the mechanical property prediction model built based on XGBoost has high prediction accuracy and can be used as a surrogate model for the fitness function during the optimization process to guide the search direction of the composition design scheme. Meanwhile, the solution set of the multi-objective optimization was sorted with weight coefficients of 0.33, 0.33, and 0.34 respectively, and 20 composition design schemes with the best overall performance were selected. Comparison was made with historical production data of AH36 steel, a commonly used marine steel. The three key performance ranges of interest in this embodiment are shown in Table 2. Table 2: Comparison of the performance range of the composition optimization scheme and historical AH36 steel

[0128] As shown in Table 2, after introducing the welding sensitivity index Pcm, the optimized scheme can still maintain high yield strength and low-temperature impact energy while achieving a lower sensitivity coefficient. From the performance range distribution analysis, the optimization results of this embodiment are more suitable for customized designs for service scenarios. The 20 design schemes with the best overall performance, according to the composition fluctuation range, are given in Table 3, which shows the composition optimization design scheme range given by the algorithm of this embodiment. Table 3: Range of optimized design schemes given in this embodiment according to preset weights

[0129] This application provides a method for designing the composition of high-strength steel for ship plates based on multi-objective black-box optimization. Compared with the prior art, this application first collects historical data such as product specifications, chemical composition, process parameters, and performance indicators of high-strength steel for ship plates from the steel plant's production and manufacturing management system. After alignment and cleaning, a standard semi-structured dataset is obtained. Then, based on this dataset, the optimization objectives (maximizing yield strength, maximizing low-temperature impact energy, and minimizing weld crack sensitivity index), decision variables (chemical composition and process parameter data), and constraints (performance, element content range, process parameters, and corrosion resistance index constraints) are defined to construct a multi-objective optimization model. Then, a mechanical performance prediction model integrating multiple performances is obtained through machine learning algorithm training. Finally, the optimal solution set is obtained by iterative calculation using a multi-objective optimization algorithm guided by reference vectors, and the final composition design scheme is selected by weighting the target steel grade and service scenario. It can accurately quantify the complex mapping relationship between composition, process and performance, avoid the high cost of trial and error, and simultaneously optimize strength, toughness, weldability and corrosion resistance to match service requirements. Moreover, the optimization algorithm takes into account both global exploration and local development, efficiently obtains the optimal solution under multiple constraints, does not require manual experience derivation, has strong generalization ability, and can be extended to the composition design of other high-strength steels or special steels.

[0130] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

[0131] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0132] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

[0133] In an exemplary embodiment, a computer device is also provided, comprising a bus, a processor, a memory, and a communication interface. It may also include an input / output interface and a display device, wherein the various functional units can communicate with each other via the bus. The memory stores a computer program, and the processor executes the program stored in the memory to perform the multi-objective black-box optimization-based high-strength steel material composition design method for ship plates described in the above embodiment.

[0134] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for designing the composition of high-strength steel for ship plates based on multi-objective black-box optimization.

[0135] Through the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented in hardware or by using software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) and includes several instructions to cause a computer device (such as a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0136] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing this application.

[0137] Those skilled in the art will understand that the modules in the apparatus of the implementation scenario can be distributed within the apparatus of the implementation scenario as described, or they can be located in one or more apparatuses different from this implementation scenario, with corresponding changes. The modules of the above-described implementation scenario can be combined into one module, or they can be further divided into multiple sub-modules.

[0138] The serial numbers in this application are for descriptive purposes only and do not represent the superiority or inferiority of the implementation scenario.

[0139] The above disclosures are only a few specific implementation scenarios of this application. However, this application is not limited to these. Any variations that can be conceived by those skilled in the art should fall within the protection scope of this application.

Claims

1. A method for designing the composition of high-strength ship plate materials based on multi-objective black-box optimization, characterized in that, include: Historical data of high-strength steel materials for ship plates collected from the steel plant's production and manufacturing management system is obtained. The historical data of high-strength steel materials for ship plates is then aligned and cleaned to obtain a standard semi-structured dataset. The historical data of high-strength steel materials for ship plates includes product specification data, chemical composition data, process parameter data, and performance index data. Based on the standard semi-structured dataset, the optimization objective, decision variables, and constraints of the target steel grade are determined. A multi-objective optimization model of the target steel grade is constructed using the optimization objective, decision variables, and constraints. The optimization objective includes maximizing yield strength, maximizing low-temperature impact energy, and minimizing the weld crack sensitivity index. The decision variables include chemical composition data and process parameter data. The constraints include performance constraints, element content range constraints, process parameter constraints, and corrosion resistance index constraints. The standard semi-structured dataset is trained using machine learning algorithms to obtain the mechanical property prediction model of the target steel grade, which integrates the yield strength prediction model, tensile strength prediction model, and low-temperature impact energy prediction model. A reference vector-guided multi-objective optimization algorithm is used to iteratively calculate the multi-objective optimization model and the mechanical performance prediction model to obtain the optimal solution set. Based on the service scenarios of the target steel grade, weights are assigned, and a high-strength steel material composition design scheme for the target steel grade is selected from the optimal solution set.

2. The method according to claim 1, characterized in that, The historical data of the high-strength steel material in the ship plate is aligned and cleaned to obtain a standard semi-structured dataset, including: The historical data of the high-strength steel material for ship plates was aligned in the order of product specifications, chemical composition, key process parameters, and mechanical properties to obtain semi-structured data. ,in, Let represent the i-th steel plate sample, and n represent the number of steel plate samples; Identify at least one missing feature value in the semi-structured data, and calculate the missing rate for each missing feature value; The missing feature values ​​with a missing rate greater than or equal to a preset missing threshold among the at least one missing feature values ​​are deleted from the semi-structured data to obtain the deleted semi-structured data. Select missing feature values ​​with a missing rate less than the preset missing threshold from the at least one missing feature value to obtain at least one target missing feature value. Obtain the average value of the same steel grade data corresponding to each target missing feature value. Fill each target missing feature value with the average value of the same steel grade data corresponding to each target missing feature value in the semi-structured data after deletion to obtain the semi-structured data after missing processing. Multiple continuous feature fields were identified in the semi-structured data after missing data processing; For each continuous feature field, the mean and standard deviation of the continuous feature field are calculated. Based on the standard deviation criterion, the outlier identification interval of the continuous feature field is determined using the mean and standard deviation of the continuous feature field. ,in, This represents the mean. Indicates standard deviation; If any of the data points included in the continuous feature field are within the outlier identification range of the continuous feature field, then the continuous feature field will be deleted from the semi-structured data after the missing data processing. Each continuous feature field in the semi-structured data after missing data processing is processed sequentially to obtain the standard semi-structured dataset.

3. The method according to claim 1, characterized in that, The mechanical property prediction model for the target steel grade is obtained by training the standard semi-structured dataset using a machine learning algorithm, integrating the yield strength prediction model, tensile strength prediction model, and low-temperature impact energy prediction model. This includes: The standard semi-structured dataset is processed using the K-means clustering algorithm to obtain the main dataset and the auxiliary dataset. The main dataset is divided into training subsets according to a preset ratio. and test subset ,in, This indicates the number of samples in the training subset. This indicates the number of samples in the test subset; The training subset and the auxiliary dataset are used as the training set. , This indicates the number of samples in the training set; The chemical composition data and process parameter data in the training set are used as input features, and the performance index data in the training set are used as output labels. The output labels include yield strength, tensile strength, and low-temperature impact energy. Using the input features and output labels, an XGBoost model is trained to obtain the yield strength prediction model, tensile strength prediction model, and low-temperature impact energy prediction model for the target steel grade. in, This represents the yield strength prediction model. This represents the tensile strength prediction model. This refers to the low-temperature impact energy prediction model. This represents the input feature. This indicates the yield strength label data in the output label. This represents the measured yield strength value corresponding to the i-th training sample in the training set. This indicates the tensile strength label data in the output label. This represents the measured tensile strength value corresponding to the i-th training sample in the training set. This indicates the low-temperature impact energy tag data in the output tag. This represents the measured value of the low-temperature impact energy corresponding to the i-th training sample in the training set; The yield strength prediction model, tensile strength prediction model, and low-temperature impact energy prediction model of the target steel grade are integrated into a mechanical property prediction model for the target steel grade.

4. The method according to claim 3, characterized in that, The standard semi-structured dataset is processed using the K-means clustering algorithm to obtain a main dataset and an auxiliary dataset, including: The selection criteria for steel material thickness are determined based on the application scenario of the target steel grade. Select sample datasets that meet the steel material thickness selection criteria from the standard semi-structured dataset. , This represents the i-th steel plate sample. Indicates the number of steel plate samples after screening; Obtain a subset of steel grade numbers, wherein the subset of steel grade numbers includes multiple steel grade numbers; The sample dataset is subjected to multi-dimensional mean calculation based on the specified steel grade subset, generating a mean vector for each steel grade. in, Let represent the mean vector of the j-th steel grade. This represents the arithmetic mean of the j-th steel grade on the k-th attribute. represents the number of steel grades, and p represents the dimension of the mean vector; The K-means clustering algorithm is used to perform unsupervised clustering on the mean vectors of the multiple steel grades to obtain multiple clustering results. The clustering result corresponding to the target steel grade is selected from the multiple clustering results as the target clustering result. The data corresponding to the target steel grade in the target clustering results are used as the main dataset. The data in the target clustering results, excluding the data corresponding to the target steel grade, are used as the auxiliary dataset. , This indicates the number of samples in the main dataset. This indicates the number of samples in the auxiliary dataset.

5. The method according to claim 3, characterized in that, The method further includes: The performance of the yield strength prediction model, the tensile strength prediction model, and the low-temperature impact energy prediction model is evaluated using the test subset, respectively, to obtain the key evaluation indicators corresponding to the yield strength prediction model, the tensile strength prediction model, and the low-temperature impact energy prediction model. The key evaluation indicators include root mean square error, mean absolute error, and coefficient of determination. If the key evaluation index corresponding to the yield strength prediction model does not meet the key evaluation index verification conditions and / or the key evaluation index corresponding to the tensile strength prediction model does not meet the key evaluation index verification conditions and / or the key evaluation index corresponding to the low temperature impact energy prediction model does not meet the key evaluation index verification conditions, then the XGBoost model is retrained using the input features and the output labels. The key evaluation index verification conditions include root mean square error less than or equal to the root mean square error threshold, mean absolute error less than or equal to the mean absolute error, and coefficient of determination greater than or equal to the coefficient of determination threshold.

6. The method according to claim 1, characterized in that, The reference vector-guided multi-objective optimization algorithm iteratively calculates the multi-objective optimization model and the mechanical performance prediction model to obtain the optimal solution set, including: The population size, maximum number of iterations, maximum number of evaluations, and proportion of individuals in fractal random walks are set, and the proportion of individuals generated by diffusion-guided generation is determined based on the maximum number of evaluations. The Latin hypercube sampling method is used to generate the initial population in the decision variable space of the multi-objective optimization model. ,in, Let N represent the i-th individual, and N represent the population size. The individual represents a high-strength steel material composition design scheme for ship plates of the target steel grade. The high-strength steel material composition design scheme for ship plates includes the composition value of each chemical component, the parameter value of the finishing rolling start temperature, the parameter value of the start cooling temperature, and the parameter value of the final cooling temperature. The Denniss method is used to generate a uniformly distributed set of reference vectors in the objective variable space of the multi-objective optimization model. ,in, This represents the Kth reference vector; For the current iteration, the mechanical property prediction model is invoked to calculate the predicted yield strength, tensile strength, and low-temperature impact energy for each individual in the current population. The welding crack sensitivity index for each individual is then calculated. Finally, the predicted yield strength, low-temperature impact energy, and welding crack sensitivity index are used to construct the fitness vector for each individual. , This represents the predicted yield strength value of the i-th individual at the current iteration number t. This represents the predicted value of the cryogenic shock energy for the i-th individual at the current iteration number t. Let represent the welding crack sensitivity index of the i-th individual at the current iteration number t, and the tensile strength prediction value of each individual meets the constraints of the multi-objective optimization model. Based on the positional relationship between the fitness vector of each individual and the set of reference vectors, calculate the set of APD values ​​for each individual; A dual-channel strategy of fractal random walk and conditional diffusion model is adopted to generate offspring population based on the set of APD values ​​of each individual; The mechanical property prediction model is invoked to calculate the predicted yield strength, tensile strength, and low-temperature impact energy of each offspring individual in the offspring population. The welding crack sensitivity index of each offspring individual is calculated. The predicted yield strength, low-temperature impact energy, and welding crack sensitivity index of each offspring individual are used to form the fitness vector of each offspring individual. The constraints of the multi-objective optimization model are used to detect the fitness vector and tensile strength prediction of each offspring individual. If the detection passes, the current population and the offspring population are combined into a merged population, and the RVEA algorithm is used to select multiple new individuals from the merged population as the next generation population. The reference vector set for the current iteration number is updated to obtain the reference vector set for the next iteration number. in, This represents the i-th reference vector in the set of reference vectors for the next iteration number t+1. This represents the i-th reference vector in the set of reference vectors at the current iteration number t. This represents the Hadamard product operator. This represents the vector formed by selecting the maximum value from the fitness vectors of each individual at the current iteration number t. This represents the vector formed by selecting the minimum value from the fitness vectors of each individual at the current iteration number t; Count the number of evaluations for the fitness function; If the number of evaluations of the fitness function is less than the maximum number of evaluations, then the next generation population and the reference vector set of the next iteration number are used to enter the next round of iteration calculation; If the number of evaluations of the fitness function is equal to the maximum number of evaluations, then the next generation population is taken as the optimal solution set, and each individual in the optimal solution set represents a composition design scheme for the target steel grade.

7. The method according to claim 6, characterized in that, The step of calculating the APD value set for each individual based on the positional relationship between the fitness vector of each individual and the reference vector set includes: The fitness vector of each individual is normalized to obtain the target vector of each individual. in, Let represent the target vector of the i-th individual at the current iteration number t. This represents the fitness vector of the i-th individual at the current iteration number t. This represents the vector formed by selecting the minimum value from the fitness vectors of each individual at the current iteration number t; The angle values ​​between different reference vectors are calculated using the aforementioned set of reference vectors. in, This represents the angle between the i-th reference vector and the j-th reference vector. This represents the i-th reference vector in the set of reference vectors at the current iteration number t. This represents the j-th reference vector in the set of reference vectors at the current iteration number t; For each reference vector, multiple angle values ​​between the reference vector and other reference vectors are extracted from the angle values ​​between the different reference vectors. The angle value with the smallest value among the multiple angle values ​​is selected as the target angle value of the reference vector. The other reference vectors are multiple reference vectors in the reference vector set other than the reference vector. Calculate the angle between the target vector of each individual and multiple reference vectors. in, This represents the angle between the i-th individual and the j-th reference vector. Let represent the target vector of the i-th individual at the current iteration number t. This represents the j-th reference vector in the set of reference vectors at the current iteration number t; The APD value between each individual and the multiple reference vectors is calculated using the angle between the target vector of each individual and the multiple reference vectors, the target angle value of each reference vector, and the target vector of each individual. in, This represents the APD value between the i-th individual and the j-th reference vector, 3 represents the number of optimization objectives, and t represents the current iteration number. Indicates the maximum number of iterations. This represents the angle between the i-th individual and the j-th reference vector. Let represent the target vector of the i-th individual at the current iteration number t. This represents the target angle value of the j-th reference vector. The coefficients represent user-defined values, N represents the population size, and K represents the number of reference vectors. The APD value between each individual and the plurality of reference vectors is taken as the APD value set of each individual.

8. The method according to claim 6, characterized in that, The dual-channel strategy employing fractal random walk and conditional diffusion models generates a offspring population based on the APD value set of each individual, including: For each individual, the APD value with the smallest value is selected from the individual's set of APD values ​​as the target APD value for that individual. in, This represents the target APD value for the i-th individual. The APD value between the i-th individual and the j-th reference vector is represented by N, where N represents the population size. The product of the population size and the proportion of the fractal random walk individuals is used as the first quantity; The individuals in the current population are sorted in descending order of their target APD values. Starting from the first individual in the sorting result, a first number of individuals are selected as parent individuals for the fractal random walk. Fractal motion is used to perturb the fractal dimension of each parent individual to obtain the first number of child individuals generated by the fractal random walk. in, This represents the i-th offspring generated by the fractal random walk in the next iteration t+1. This represents the i-th parent individual in the current iteration t. This represents a mask vector of length m. This represents the Hadamard product operator. The scaling factor of the Levy distribution. This represents the index that controls the Levy distribution. The scaling factor representing the Gaussian distribution. For the parameters of the Gaussian distribution, Indicates the optimal parent individual position. Indicates standard deviation; The product of the population size and the proportion of individuals generated by the diffusion guidance is used as the second quantity; The data vector and the target APD value of each individual are merged to obtain the extended vector of each individual. in, This represents the expansion vector of the i-th individual at the current iteration number t. This represents the data vector of the i-th individual at the current iteration number t. This represents the target APD value of the i-th individual at the current iteration number t, where m represents the dimension of the decision variable; The expansion vector of each individual is input into the conditional diffusion model to obtain the second number of offspring individuals generated by the conditional diffusion model. in, This represents the i-th offspring generated by the conditional diffusion model in the next iteration t+1. Represents the extended vector set, Let N represent the expansion vector of the i-th individual at the current iteration number t, and N represent the population size. The first number of offspring individuals generated by fractal random walk and the second number of offspring individuals generated by conditional diffusion model are taken as the offspring population.

9. The method according to claim 6, characterized in that, The environment selection using the RVEA algorithm selects multiple new individuals from the merged population as the next generation population, including: Based on the positional relationship between the fitness vector of each new individual in the merged population and the set of reference vectors, calculate the APD value between each new individual and the plurality of reference vectors; For each reference vector, determine the APD value between each new individual and the reference vector, and take the new individual with the smallest APD value as the target individual; Based on the APD value between each new individual and the multiple reference vectors, each reference vector is processed to obtain multiple target individuals, and the multiple target individuals are used as the initial parent population. Count the number of individuals in the initial parent population; When the number of individuals in the initial parent population is less than the population size, the new individual with the smallest APD value is selected from the other new individuals and added to the initial parent population, until the number of individuals in the initial parent population after addition is equal to the population size, thus obtaining the next generation population. The other new individuals are multiple new individuals in the merged population other than the multiple target individuals. When the number of individuals in the initial parent population is equal to the population size, the initial parent population is used as the next generation population.

10. The method according to claim 6, characterized in that, After the fitness vector and tensile strength prediction value of each offspring individual are detected using the constraints of the multi-objective optimization model, the method further includes: If the test fails, the offspring individuals that fail the test are identified and deleted. Determine the generation strategy corresponding to the offspring individuals that fail the detection, and regenerate offspring individuals using the generation strategy, wherein the generation strategy is a fractal random walk or a conditional diffusion model.

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