A method and device for constructing a high-dimensional approximate model in ship type optimization

Abstract

The application provides a method and device for constructing a high-dimensional approximate model in ship type optimization, and relates to the technical field of three-dimensional modeling. The method comprises the following steps: determining a target response function of a ship type optimization problem and constructing a ship type parameterization model, an optimization variable set for ship type optimization and a value range of each variable; decomposing the optimization variable set into a plurality of sub-variable combinations according to the coupling relationship between the optimization variables, and constructing a plurality of sub-functions according to the number of variables contained in each sub-variable combination; selecting sample points in the corresponding variable space based on a test design method for each sub-problem corresponding to each sub-function, and constructing a low-dimensional mathematical expression model of the sub-problem; and adding all the constructed mathematical expression models according to the combination form corresponding to the sub-functions to obtain the overall mathematical model of the original high-dimensional ship type optimization problem. The application has the dimension decomposition capability and the local precision control capability to solve the problem that the current high-dimensional response function modeling is difficult to apply.

Description

Technical Field

[0001] This application relates to the technical field of three-dimensional modeling, specifically to a method and apparatus for constructing a high-dimensional approximate model in ship hull optimization. Background Technology

[0002] As ship design tasks increasingly demand the coordinated optimization of multiple performance aspects such as resistance characteristics, stability indicators, maneuverability, and structural strength, the number of optimization variables to be considered also increases. In typical application scenarios, the dimension of optimization variables often exceeds twenty dimensions. Such high-dimensional ship optimization problems place extremely high demands on the expressive power and modeling efficiency of response function models. In particular, during the process of hull surface changes, the correlation between different parameters is significantly enhanced, and the coupling structure between variables becomes complex and highly nonlinear, thus posing new challenges to response function modeling.

[0003] In existing technologies, traditional response function modeling methods such as the Kriging model, multinomial response surface model, and radial basis function model have good fitting ability and application effects when dealing with ship morphology optimization problems with low variable dimensionality. However, when the variable dimensionality increases rapidly and there are significant multivariate coupling characteristics, these models face two major drawbacks: First, the number of model parameters increases exponentially, leading to a significant increase in dependence on the number of samples, making it difficult to construct a mathematical model with stable convergence. Second, the complex interactions between high-dimensional variables make it difficult for traditional models to fully capture the combined effect of various variable combinations on the response function, resulting in a sharp increase in model fitting error and severe local response distortion. Therefore, traditional modeling methods are gradually becoming ineffective when facing high-dimensional ship morphology optimization problems, and there is an urgent need to construct a new modeling scheme with dimensionality decomposition ability and local accuracy control capability to solve the problem that current high-dimensional response function modeling is difficult to apply. Summary of the Invention

[0004] This application provides a method and apparatus for constructing a high-dimensional approximate model in ship hull optimization, which has the ability to decompose dimensions and control local precision, so as to solve the problem that current high-dimensional response function modeling is difficult to apply.

[0005] The first aspect of this application provides a method for constructing a high-dimensional approximation model in ship hull optimization, the method comprising:

[0006] Determine the objective response function of the ship morphology optimization problem and construct a parametric model of the ship morphology, and determine the set of optimization variables used for ship morphology optimization and the range of values ​​for each variable;

[0007] Based on the coupling relationship between the optimization variables, the set of optimization variables is decomposed to obtain several sub-variable combinations. Based on the number of variables contained in each sub-variable combination, multiple sub-functions are constructed to represent the independent or coupled effects of different variable combinations on the output value of the target response function.

[0008] For each sub-problem corresponding to the sub-function, sample points are selected in the corresponding variable space based on the experimental design method to construct the mathematical expression model of the first dimension of the sub-problem;

[0009] During the construction process, the convergence judgment criterion is used to continuously determine whether each mathematical expression model has reached the convergence standard. If it has not converged, the mathematical expression model is iteratively updated until the convergence criterion is met.

[0010] All the constructed mathematical expression models are summed according to the combination forms corresponding to the sub-functions to obtain the overall mathematical model of the original second-dimensional ship shape optimization problem, wherein the first dimension is lower than the second dimension.

[0011] Based on the above technical solutions, preferably, the step of determining the objective response function of the ship morphology optimization problem and constructing a parametric model of the ship morphology, and determining the set of optimization variables used for ship morphology optimization and the value range of each variable, specifically includes:

[0012] Based on the design requirements and operating conditions of specific ship types, multiple performance objectives for hull optimization are defined.

[0013] One or more performance targets that meet the preset requirements are selected from the multiple performance targets as optimization targets, thereby establishing a target response function for evaluating ship performance;

[0014] A parametric modeling method is used to formally represent the hull geometry. The parametric modeling method satisfies the requirements of parameter controllability, hull shape continuity, and consistency of feasible geometric constraints. The parametric modeling method maps the hull surface geometry to a set of finite parametric variables, thereby forming a parametric expression.

[0015] After completing the parametric modeling of the hull, based on the sensitivity of each parameter in the hull optimization design to the target response function and the actual physical meaning of the variables, all optimization variables constituting the set of optimization variables are determined. The optimization variables include geometric parameters that control the changes in hull lines and auxiliary structural parameters that affect performance.

[0016] A range of values ​​is set for each of the optimization variables, and the range of values ​​is determined comprehensively based on design specifications, structural constraints, performance boundaries and practical engineering experience.

[0017] Based on the above technical solutions, preferably, after summing all the constructed mathematical expression models according to the combination forms corresponding to the sub-functions to obtain the overall mathematical model of the original second-dimensional ship shape optimization problem, the method further includes:

[0018] Multiple test functions with different numbers of variables and complex coupling relationships are selected as evaluation benchmarks. The response functions of the test functions have known analytical expressions and have different degrees of variable interaction characteristics in structure, so as to form a test set covering various response behaviors such as single variable dominance, multivariate coupling, and local extremum complexity.

[0019] For each of the test functions, a mathematical model is constructed to obtain the test mathematical model;

[0020] After the test mathematical models are constructed, each test mathematical model is evaluated using a uniformly sampled test sample set. The evaluation metrics include the coefficient of determination R. 2 The relative mean absolute error (RAAE) and the relative maximum absolute error (RMAE) are also considered.

[0021] Based on the above technical solutions, preferably, the optimization variable set is decomposed according to the coupling relationship between the optimization variables to obtain several sub-variable combinations, and multiple sub-functions are constructed according to the number of variables contained in each sub-variable combination to represent the independent or coupled influence of different variable combinations on the output value of the target response function, specifically including:

[0022] By using the methods for identifying the interrelationships between the optimization variables, a systematic analysis is performed on all the optimization variables to identify the interaction relationships between each optimization variable in the target response function. Specifically, a preliminary sample response dataset of the target response function with respect to all the optimization variables is constructed, and based on the preliminary sample response dataset, the marginal impact of each optimization variable on the target response function when other optimization variables remain constant is analyzed, as well as the trend of combined response changes to the target response function when multiple optimization variables change in tandem. It is determined whether there is an interaction effect between the optimization variables. If the interaction effect exists, multiple optimization variables are classified as a combination of coupled variables.

[0023] Based on the identification results of the coupling variable combination, the set of optimization variables is decomposed into several variable subsets. Each variable subset consists of a set of optimization variables with interactive effects, and it is ensured that each optimization variable belongs to at least one of the variable subsets.

[0024] Next, according to the number of optimization variables contained in the variable subset, all the variable subsets are classified into one-variable subsets, two-variable subsets, and multi-variable subsets, and corresponding first-order sub-functions, second-order sub-functions, and multi-order sub-functions are constructed. Each sub-function serves as a local response mapping of the target response function under the corresponding variable subset.

[0025] Based on the above technical solutions, preferably, the step of selecting sample points in the corresponding variable space based on the experimental design method to construct a mathematical expression model of the first dimension of the sub-problem for each sub-function specifically includes:

[0026] For each of the defined variable subsets, the variable space is defined as a parameter domain spanned by all the optimized variables in the variable subsets, and the input domain of the sub-functions corresponding to the variable subsets is defined.

[0027] Based on the structural characteristics of the variable space and the dimension of the sub-function, an experimental design method is selected to generate the sample point set;

[0028] The sample point set is generated within the variable space using the selected experimental design method, and the target response function value of the sub-function at the sample point is calculated or simulated for each sample point in the sample point set, thereby forming the input-output pair of the sample points;

[0029] Based on multiple input-output pairs, a mathematical expression model of the sub-function is constructed. The mathematical expression model expresses the input-output mapping relationship of the sub-function in the variable space. According to the mathematical expression model, the dimension of the input variables is limited to the optimized variables in the variable subset.

[0030] Based on the above technical solution, preferably, during the construction process, a convergence criterion is used to continuously determine whether each mathematical expression model has reached the convergence standard. If convergence is not achieved, the mathematical expression model is iteratively updated until the convergence criterion is met. Specifically, this includes:

[0031] A convergence criterion is set for the mathematical expression model corresponding to each sub-function. The convergence criterion is used to evaluate the degree of approximation of the mathematical expression model to the target response function in the variable space.

[0032] After each round of experimental design samples is constructed, the mathematical expression model is updated using the new experimental design samples and the corresponding target response values, and the updated mathematical expression model is cross-validated to extract the error index value.

[0033] The error index value is compared with a preset error tolerance threshold. If the error index value is within the error tolerance threshold, the mathematical expression model is determined to have converged.

[0034] Based on the above technical solutions, preferably, the step of summing all the constructed mathematical expression models according to the combination forms corresponding to the sub-functions to obtain the overall mathematical model of the original second-dimensional ship shape optimization problem specifically includes:

[0035] The mathematical expression models are structurally combined according to the variable dimension hierarchy of the sub-functions, specifically including the mathematical expression models of the first-order sub-functions, the second-order sub-functions, and the multi-order sub-functions, which respectively represent the response contributions generated by the influence of a single variable, the bidirectional interaction between variables, and the multivariate coupling effect.

[0036] When performing the summation operation, the functional form of each of the mathematical expression models remains unchanged, and all the mathematical expression models take the variables that are actually covered in the variable space as independent variables. The superposition process does not introduce dimensional misalignment or repeated calculation of variables. The overall mathematical model is the algebraic sum of all the constructed mathematical expression models.

[0037] A second aspect of this application provides an apparatus for constructing a high-dimensional approximation model in ship morphology optimization. The apparatus is used to execute a method for constructing a high-dimensional approximation model in ship morphology optimization as described in any of the above-described methods. The apparatus includes an acquisition module, a processing module, and an output module, wherein:

[0038] The acquisition module is used to determine the objective response function of the ship type optimization problem and construct a ship type parameterized model, and to determine the set of optimization variables for ship type optimization and the value range of each variable;

[0039] The processing module is used to decompose the set of optimization variables according to the coupling relationship between the optimization variables to obtain several sub-variable combinations, and to construct multiple sub-functions according to the number of variables contained in each sub-variable combination, so as to represent the independent or coupled influence of different variable combinations on the output value of the target response function.

[0040] The processing module is used to select sample points in the corresponding variable space based on the experimental design method for each sub-problem corresponding to the sub-function, and construct a mathematical expression model of the first dimension of the sub-problem.

[0041] The processing module is used to continuously determine whether each mathematical expression model has reached the convergence standard during the construction process by using a convergence judgment criterion. If it has not converged, it continues to iteratively update the mathematical expression model until the convergence criterion is met.

[0042] The output module is used to sum all the completed mathematical expression models according to the combination form corresponding to the sub-functions to obtain the overall mathematical model of the original second-dimensional ship shape optimization problem, wherein the first dimension is lower than the second dimension.

[0043] Based on the above technical solutions, preferably, the processing module is used to determine multiple performance objectives for hull optimization based on the design requirements and operating conditions of a specific ship type.

[0044] The acquisition module is used to select one or more performance targets that meet the preset requirements from the plurality of performance targets as optimization targets, thereby establishing a target response function for evaluating ship performance;

[0045] The processing module is used to formally express the hull geometry using a parametric modeling method. The parametric modeling method satisfies requirements such as parameter controllability, hull shape continuity, and consistency of feasible geometric constraints. The parametric modeling method maps the hull surface geometry to a set of finite parametric variables, thereby forming a parametric expression.

[0046] The processing module is used to determine all optimization variables constituting the set of optimization variables after completing the parametric modeling of the hull, based on the sensitivity of each parameter in the hull optimization design to the target response function and the actual physical meaning of the variables. The optimization variables include geometric parameters that control the change of hull lines and auxiliary structural parameters that affect performance.

[0047] The processing module is used to set a value range for each of the optimization variables. The value range is determined comprehensively based on design specifications, structural constraints, performance boundaries and practical engineering experience.

[0048] Based on the above technical solutions, preferably, the acquisition module is used to select multiple test functions with different numbers of variables and complex coupling relationships as evaluation benchmarks. The response functions of the test functions have known analytical expressions and have different degrees of variable interaction characteristics in structure, so as to form a test set covering a variety of response behaviors such as single variable dominance, multi-variable coupling, and local extremum complexity.

[0049] The acquisition module is used to construct a mathematical model for each of the test functions to obtain a test mathematical model.

[0050] The processing module is used to evaluate each of the test mathematical models after the test mathematical models are constructed, using a uniformly sampled test sample set. The evaluation index includes the coefficient of determination R. 2 The relative mean absolute error (RAAE) and the relative maximum absolute error (RMAE) are also considered.

[0051] Based on the above technical solution, preferably, the processing module is used to systematically analyze all the optimization variables through the means of identifying the interrelationships between the optimization variables, so as to identify the interaction relationship between each optimization variable in the target response function. Specifically, it constructs a preliminary sample response dataset of the target response function with respect to all the optimization variables, and analyzes the marginal impact of each optimization variable on the target response function when other optimization variables remain constant, as well as the combined response change trend of the target response function when multiple optimization variables change in tandem, based on the preliminary sample response dataset. It then determines whether there is an interaction effect between the optimization variables, and if such an interaction effect exists, classifies the multiple optimization variables as a combination of coupled variables.

[0052] The processing module is used to decompose the set of optimization variables into several subsets of variables based on the identification results of the combination of coupling variables. Each subset of variables consists of a set of optimization variables with interactive effects, and ensures that each optimization variable belongs to at least one subset of variables.

[0053] The processing module is then used to classify all the variable subsets into one-variable subsets, two-variable subsets, and multi-variable subsets according to the number of optimization variables contained in the variable subsets, and construct first-order sub-functions, second-order sub-functions, and multi-order sub-functions accordingly. Each sub-function serves as a local response mapping of the target response function under the corresponding variable subset.

[0054] Based on the above technical solutions, preferably, the processing module is used to define the variable space for each of the divided variable subsets, wherein the variable space is a parameter domain spanned by all the optimized variables in the variable subset, and to define the input domain of the sub-function corresponding to the variable subset.

[0055] The processing module is used to select an experimental design method to generate a sample point set based on the structural characteristics of the variable space and the dimension of the sub-function.

[0056] The processing module is used to generate the sample point set in the variable space using the selected experimental design method, and to calculate or simulate the target response function value of the sub-function at each sample point in the sample point set, thereby forming the input-output pair of the sample points;

[0057] The processing module is used to construct a mathematical expression model of the sub-function based on multiple input-output pairs. The mathematical expression model expresses the input-output mapping relationship of the sub-function in the variable space. According to the mathematical expression model, the dimension of the input variables is limited to the optimized variables in the variable subset.

[0058] Based on the above technical solutions, preferably, the processing module is used to set a convergence judgment criterion for the mathematical expression model corresponding to each sub-function, and the convergence judgment criterion is used to evaluate the degree of approximation of the mathematical expression model to the target response function in the variable space;

[0059] The processing module is used to update the mathematical expression model with the new experimental design sample and the corresponding target response value after each round of experimental design sample construction is completed, and to perform cross-validation on the updated mathematical expression model to extract the error index value.

[0060] The processing module is used to compare the error index value with a preset error tolerance threshold. If the error index value is within the error tolerance threshold, it is determined that the mathematical expression model has converged.

[0061] Based on the above technical solutions, preferably, the processing module is used to structurally combine the mathematical expression model according to the variable dimension hierarchy of the sub-functions, specifically including the mathematical expression model of the first-order sub-function, the mathematical expression model of the second-order sub-function, and the mathematical expression model of the multi-order sub-function, which respectively represent the response contributions generated by the single variable influence, the bidirectional interaction between variables, and the multi-variable coupling effect.

[0062] The processing module is used to maintain the functional form of each of the mathematical expression models unchanged when performing the summation operation, and all the mathematical expression models take the variables that are actually covered in the variable space as independent variables. The superposition process does not introduce dimensional misalignment or repeated calculation of variables. The overall mathematical model is the algebraic sum of all the constructed mathematical expression models.

[0063] A third aspect of this application provides an electronic device including a processor, a memory, a user interface, and a network interface, wherein the memory is used to store instructions, the user interface and the network interface are both used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to cause the electronic device to perform the method as described in any of the foregoing.

[0064] A fourth aspect of this application provides a computer-readable storage medium storing instructions that, when executed, perform the method described in any of the preceding descriptions.

[0065] In summary, one or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0066] 1. This application decomposes the modeling task of the all-variable response function in the high-dimensional ship hull optimization problem into multiple low-dimensional sub-problems. It employs a variable coupling relationship identification method to divide the set of optimization variables into several combinations of sub-variables, and constructs first-order, second-order, and multi-order sub-functions respectively, thereby achieving a structured decomposition of complex high-dimensional nonlinear response relationships. Each sub-function independently constructs a mathematical expression model in its local variable space. Convergence judgment criteria are formulated in conjunction with error evaluation indicators, and iterative optimization is performed to ensure controllable accuracy of the local model. Finally, the overall response function model is reconstructed through the algebraic summation of all sub-functions. This significantly improves modeling accuracy and computational efficiency without increasing the number of sample points, fully demonstrating its ability to decompose dimensions and control local accuracy. It effectively overcomes the parameter explosion and accuracy decay problems faced by traditional methods in high-dimensional modeling.

[0067] 2. This technical solution clarifies the multiple performance indicators of ships in actual use environments and combines parametric modeling methods to map complex hull geometry into a finite-dimensional expression of optimization variables, thereby constructing a target response function. This achieves a systematic transformation from hull performance requirements to controllable variables, ensuring that the optimization modeling has physical consistency, structural integrity, and variable adjustability.

[0068] 3. By introducing standard test functions with known structures, a unified modeling and evaluation mechanism is established, using R... 2 The performance of the modeling method was quantitatively evaluated using metrics such as RAAE and RMAE, which effectively verified the accuracy, stability and adaptability of the method under different variable dimensions and coupling structures, demonstrating its potential for application in a wide range of engineering problems.

[0069] 4. By optimizing the interaction between variables, a variable coupling relationship graph is constructed, and the complex variable set is decomposed into multiple variable subsets with clear interaction structures. Then, first-order to multi-order sub-functions are constructed, systematically realizing the structural deconstruction of high-dimensional response functions, reducing the modeling dimension and function complexity, and laying the foundation for accurate modeling.

[0070] 5. Experimental design and sample generation are performed independently within the variable space of each subset of variables, and local mathematical expression models are constructed using input-output pairs to ensure that each sub-function model only covers relevant variables, thereby improving sample utilization efficiency and modeling accuracy, while providing modular components for the structural combination of the overall model.

[0071] 6. By setting convergence criteria and extracting error indicators based on cross-validation, a clear error control mechanism is established. During the iteration process, the mathematical expression model of each sub-function is dynamically optimized to ensure that all sub-models have stable convergence characteristics in their respective variable spaces, thereby significantly improving the prediction accuracy and robustness of the overall model.

[0072] 7. All mathematical expression models are structurally combined according to variable dimensions. The overall response function model is constructed by algebraically superimposing first-order, second-order, and multi-order models. The consistency of independent variables and independence of function form of each model are strictly maintained to avoid variable repetition and dimension mismatch, and to ensure that the overall mathematical model has logical closure, expression integrity, and combinatorial analyzability. Attached Figure Description

[0073] Figure 1 This is a flowchart illustrating a method for constructing a high-dimensional approximate model in ship hull optimization, as disclosed in an embodiment of this application.

[0074] Figure 2 This is a schematic diagram of a module of a device for constructing a high-dimensional approximate model in ship morphology optimization, as disclosed in an embodiment of this application.

[0075] Figure 3 This is a schematic diagram of the structure of an electronic device disclosed in an embodiment of this application.

[0076] Explanation of reference numerals in the attached drawings: 201, acquisition module; 202, processing module; 203, output module; 301, processor; 302, communication bus; 303, user interface; 304, network interface; 305, memory. Detailed Implementation

[0077] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0078] In the description of the embodiments of this application, the words "for example" or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design that is described as "for example" or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design options. Rather, the use of the words "for example" or "for instance" is intended to present the relevant concepts in a specific manner.

[0079] In the description of the embodiments of this application, the term "multiple" means two or more. For example, multiple systems means two or more systems, and multiple screen terminals means two or more screen terminals. 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 indicated technical features. Thus, a feature defined with "first" or "second" may explicitly or implicitly include one or more of that feature. The terms "comprising," "including," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0080] With the increasing demand for multi-performance synergistic optimization in ship design tasks, the dimensionality of optimization variables involved in ship hull optimization problems has significantly increased, often exceeding twenty dimensions, and exhibiting highly nonlinear and complex coupled structures. This leads to traditional response function modeling methods such as Kriging models, polynomial response surface models, and radial basis function models facing problems of parameter explosion and increased sample dependence in such high-dimensional scenarios. At the same time, it is difficult to accurately characterize the combined effect of multiple variables on the response function, resulting in amplified model errors and severe local distortion. Therefore, there is an urgent need for a new response function modeling method with dimensional decomposition and local precision control capabilities to overcome the current technical bottlenecks.

[0081] This embodiment discloses a method for constructing a high-dimensional approximation model in ship hull optimization, referring to... Figure 1 This includes the following steps S110-S150:

[0082] S110, determine the objective response function of the ship type optimization problem and construct a ship type parameterized model, and determine the set of optimization variables used for ship type optimization and the value range of each variable.

[0083] The method for constructing a high-dimensional approximation model in ship hull optimization disclosed in this application is applied to a server. The server includes, but is not limited to, electronic devices such as mobile phones, tablets, wearable devices, and PCs (Personal Computers), and can also be a backend server running the method for constructing a high-dimensional approximation model in ship hull optimization. The server can be implemented using a standalone server or a server cluster composed of multiple servers.

[0084] In one possible implementation, the objective response function of the hull optimization problem is determined and a parametric model of the hull is constructed. The set of optimization variables and the value range of each variable are determined. Specifically, this includes: identifying multiple performance objectives for hull optimization based on the design requirements and operating conditions of a specific ship type; selecting one or more performance objectives that meet preset requirements as optimization objectives, thereby establishing an objective response function for evaluating hull performance; formally expressing the hull geometry using parametric modeling methods, which satisfy requirements such as parameter controllability, hull shape continuity, and consistency of feasible geometric constraints. Specifically, the parametric modeling method maps the hull surface geometry to a finite set of parametric variables, thus forming a parametric expression; after completing the parametric modeling of the hull, determining all optimization variables constituting the set of optimization variables based on the sensitivity of each parameter in the hull optimization design to the objective response function and the actual physical meaning of the variables. These optimization variables include geometric parameters controlling hull line changes and auxiliary structural parameters affecting performance; and setting a value range for each optimization variable, which is comprehensively determined based on design specifications, structural constraints, performance boundaries, and practical engineering experience.

[0085] Specifically, when defining the design requirements and operating conditions of a vessel type, priority should be given to collecting parameter data including vessel purpose, design speed, displacement, full-load draft, navigation zone class, and operating environment. Based on the design specifications and technical requirements, the performance indicators that must be met should be extracted. These indicators typically cover dimensions such as hydrodynamic performance, structural safety, and maneuverability. A list of performance indicators should be established, with their design constraint levels and optimization priorities marked. A multi-performance weighting method should be used to determine the set of target performance parameters for optimization calculations, and preliminary quantitative processing should be performed to form the basic data structure for defining the subsequent target response function.

[0086] When selecting optimization objectives and establishing the target response function, several performance objectives with the most representative or design influence should be chosen as optimization objectives based on the aforementioned performance weighting results. For example, in the design of high-speed ships, priority should be given to minimizing resistance, while in the design of polar icebreakers, priority should be given to minimizing stability and wave load response. The target response function should adopt different levels of modeling accuracy according to the actual design stage: in the preliminary design stage, simplified empirical formulas can be used, while in the detailed design stage, accurate response values ​​need to be obtained by combining CFD calculations or structural finite element analysis simulations, and then a mathematical expression should be constructed using regression modeling or interpolation methods, thus forming a functional relationship where the input is the optimization variable and the output is the target performance index.

[0087] When constructing a parametric representation model of the ship's geometry, the hull section lines, planar lines, and waterline curves should be standardized, and the 3D shape model should be completed using surface fitting methods based on these line types. Mathematical methods that ensure continuous smoothness and parameter control should be selected, such as using NURBS modeling to define the hull surface through node vectors and control point arrays, or using a free deformation method based on radial basis functions to control line type deformation. All modeling parameters should be clearly mapped to actual structural geometric changes so that they can be effectively used in subsequent parameter optimization processes.

[0088] When identifying the set of optimized variables, the importance of each parameter should be ranked in conjunction with the sensitivity analysis process. In this process, firstly, a certain number of experimental points are generated based on the initial sample, and the corresponding target response function values ​​are calculated. Then, using Sobol global sensitivity analysis or variance decomposition based on LHS sampling, the contribution rates of each parameter to the main effects and interaction effects of the response function are statistically analyzed. Parameters whose contribution rates exceed a preset threshold are preferentially retained as main variables; parameters that do not meet the sensitivity contribution requirements are removed to avoid model redundancy. Simultaneously, control variables that have a key impact on the physical structure are retained, ultimately forming the set of optimized variables with minimal redundancy and maximum response explanatory power.

[0089] When setting the value range for each optimization variable, a triple constraint analysis should be performed on its feasible interval. First, structural limit constraints should be set according to the ship's structural design specifications (such as plate thickness, frame spacing, bilge curvature, etc.). Second, response-oriented boundaries should be calculated based on design performance boundaries (such as maximum allowable resistance, minimum stability index, etc.). Finally, reasonable median values ​​and adjustment step sizes should be determined by combining empirical data and manufacturing feasibility constraints. When necessary, mathematical inequality constraints should be introduced to express the coupling boundaries between variables, forming a set of optimization parameter space boundaries to ensure that variable combinations in the optimization process meet physical and engineering feasibility requirements. All parameter boundaries should be uniformly formatted into a data structure that can be directly called during the optimization modeling process, providing basic support for variable combination decomposition and sample point generation.

[0090] S120. Based on the coupling relationship between the optimization variables, the set of optimization variables is decomposed to obtain several combinations of sub-variables. Based on the number of variables contained in each sub-variable combination, multiple sub-functions are constructed to represent the independent or coupled influence of different combinations of variables on the output value of the target response function.

[0091] In one possible implementation, the set of optimization variables is decomposed based on the coupling relationships between them to obtain several combinations of sub-variables. Multiple sub-functions are then constructed based on the number of variables in each sub-variable combination to represent the independent or coupled effects of different variable combinations on the output value of the target response function. Specifically, this includes: performing a qualitative analysis on all optimization variables using methods to identify the interrelationships between them in the target response function; constructing a preliminary sample response dataset of the target response function with respect to all optimization variables; and analyzing the marginal impact of each optimization variable on the target response function when other optimization variables remain constant based on this preliminary sample response dataset, as well as multiple... The trend of combined response changes to the target response function when optimization variables change in tandem is analyzed to determine whether there is an interaction effect between the optimization variables. If an interaction effect exists, multiple optimization variables are classified as a combination of coupled variables. Based on the identification results of the combination of coupled variables, the set of optimization variables is decomposed into several variable subsets. Each variable subset consists of a group of optimization variables with interaction effects, and it is ensured that each optimization variable belongs to at least one variable subset. Then, according to the number of optimization variables contained in the variable subset, all variable subsets are classified into one-variable subsets, two-variable subsets, and multi-variable subsets. Correspondingly, first-order sub-functions, second-order sub-functions, and multi-order sub-functions are constructed. Each sub-function serves as a local response mapping of the target response function under the corresponding variable subset.

[0092] Specifically, when conducting a qualitative analysis of all optimization variables using methods to identify the interrelationships between optimization variables, the first step should be to use experimental design methods such as orthogonal experimental design, Latin hypercube sampling, or Sobol sequence sampling, based on the defined objective response function, to generate a certain number of sample points within the complete optimization variable space. These sample points should then be simulated or calculated to obtain the objective response function values, forming a preliminary sample response dataset. Subsequently, univariate marginal analysis and multivariate combined response trend analysis should be performed on this dataset. That is, the values ​​of other optimization variables are fixed, only one optimization variable is changed, and its independent impact on the objective response function is recorded. Then, two or more optimization variables are selected and their combined changes are observed to observe the nonlinear characteristics of the output value of the objective response function. If the output value of the objective response function exhibits a non-superposition property or shows a significant increase or reversal due to the combined changes of two or more variables, it is determined that there is an interaction effect between the variable groups, thus marking it as a coupled variable combination.

[0093] After identifying all combinations of coupled variables, the original set of optimization variables should be divided into several subsets based on their interaction structure. Each subset consists of a group of optimization variables that interact with each other in the objective response function. During the partitioning process, it should be ensured that each optimization variable participates in at least one subset to avoid missing variable influences during function modeling. The partitioning principle should prioritize interaction strength, grouping variables with significant interactions into the same subset. If some variables exhibit moderate interaction in multiple combinations, they are allowed to appear repeatedly in multiple subsets to maintain the integrity of the true interaction structure between variables.

[0094] Based on the number of optimization variables included in the variable subsets, the partitioned variable subsets are classified by order. Specifically, if a variable subset contains only one optimization variable, it is classified as a one-variable subset, and a first-order sub-function is constructed to describe the independent response characteristics of that single variable to the objective response function. If a variable subset contains two optimization variables, it is a two-variable subset, and a second-order sub-function is constructed to characterize the response pattern of that variable to the combined effect. If a variable subset contains three or more optimization variables, it is classified as a multi-variable subset, and a multi-order sub-function is constructed to express the higher-order interactive response relationships between multiple variables. Each sub-function is confined to the variable space spanned by its corresponding variable subset, serving as a mapping model of the objective response function in that local variable space. Its structure should support the subsequent sample point construction and mathematical expression modeling process, ensuring that the full-space combination expression of the original objective response function can be achieved through the decomposition modeling of sub-functions.

[0095] S130: For each sub-function and its corresponding sub-problem, sample points are selected in the corresponding variable space based on the experimental design method to construct the mathematical expression model of the first dimension of the sub-problem.

[0096] In one possible implementation, for each sub-function corresponding to a sub-problem, sample points are selected in the corresponding variable space based on an experimental design method to construct a mathematical expression model of the first dimension of the sub-problem. Specifically, this includes: defining the input domain of the sub-function corresponding to each variable subset, where the variable space is a parameter domain spanned by all optimized variables in the variable subset; selecting an experimental design method to generate a sample point set based on the structural characteristics of the variable space and the dimension of the sub-function; generating the sample point set in the variable space using the selected experimental design method, and calculating or simulating the target response function value of the sub-function at each sample point in the sample point set, thereby forming an input-output pair of the sample points; and constructing a mathematical expression model of the sub-function based on multiple input-output pairs. The mathematical expression model expresses the input-output mapping relationship of the sub-function in the variable space. According to the mathematical expression model, the dimension of the input variables is limited to the optimized variables in the variable subset.

[0097] Specifically, when defining the variable space constituted by each subset of variables, one should first extract all optimization variables contained in that subset, and then construct the parameter domain spanning that subset based on their respective defined value ranges. This parameter domain is the variable space of that subset. Within this space, each point represents a specific combination of optimization variables as input, which will serve as the input domain of the sub-function corresponding to that subset. Since the subsets of variables have different dimensions, each variable space has an independent dimensional structure and should be processed separately.

[0098] When selecting experimental design methods based on the structural characteristics of the variable space and the dimensionality of the sub-functions, the dimensionality of the variable space, the potential nonlinear relationships between variables, the required model accuracy, and sample economy should be considered. Priority should be given to design methods that can uniformly cover the variable space and have good projection characteristics. For low-dimensional spaces, orthogonal experimental design or full factorial design methods can be used, while for high-dimensional spaces, low-discrepancy sequences such as Latin hypercube sampling, Sobol sequences, or Halton sequences should be selected to ensure the representativeness of the sample distribution and the stability of the response modeling.

[0099] When generating a sample point set within the variable space, the sample size, variable value strategy, and distribution should be set according to the selected experimental design method to generate a sample point set covering the entire variable space. Then, physical simulation software, high-precision empirical models, or calculation modules should be invoked to calculate the corresponding target response function value at each sample point. Each set of sample points and its response function value together constitute an input-output pair. This input-output pair reflects the mapping behavior of the sub-function in the variable space and serves as the foundational data for constructing the mathematical expression model.

[0100] When constructing a mathematical representation model of a sub-function based on the aforementioned input-output pair, an appropriate modeling method should be selected according to the sub-function's dimension, nonlinear characteristics, and sample point size. Possible methods include multinomial regression models, radial basis function networks, support vector regression models, or Gaussian process regression models. All mathematical representation models must satisfy two basic conditions: first, the dimension of the model's input variables must be strictly limited to the optimized variables contained in the subset of variables; second, the model output should be able to accurately and stably approximate the true response value of the target response function within the variable space. The final mathematical representation model of the sub-function should possess consistency of expression, continuity of response, and composability of structure to support the subsequent model superposition and reconstruction process.

[0101] S140: During the construction process, the convergence criterion is used to continuously determine whether each mathematical expression model has reached the convergence standard. If it has not converged, the mathematical expression model is iteratively updated until the convergence criterion is met.

[0102] In one possible implementation, during the construction process, a convergence criterion is used to continuously determine whether each mathematical expression model has reached the convergence standard. If it has not converged, the mathematical expression model is iteratively updated until the convergence criterion is met. Specifically, this includes: setting a convergence criterion for the mathematical expression model corresponding to each sub-function, which is used to evaluate the degree to which the mathematical expression model approximates the target response function in the variable space; after each round of experimental design sample construction is completed, the mathematical expression model is updated using the new experimental design sample and the corresponding target response value, and cross-validation is performed on the updated mathematical expression model to extract the error index value; the error index value is compared with a preset error tolerance threshold, and if the error index value is within the error tolerance threshold, the mathematical expression model is determined to have converged.

[0103] Specifically, when setting convergence criteria for the mathematical expression model corresponding to each sub-function, the quantitative index suitable for evaluating the error of the response function should be selected as the convergence criterion based on the functional characteristics and modeling accuracy requirements of the sub-function in its variable space. Commonly used criteria include the coefficient of determination R. 2 The relative mean absolute error RAAE and the relative maximum absolute error RMAE, where R 2 The RAAE is used to measure the model’s global interpretability, the RMAE is used to evaluate the average fitting error level, and the RMAE is used to capture the local error performance at extreme response locations. Each metric needs to be set with a specific error tolerance threshold as a basis for judging whether the model accuracy meets the convergence criteria.

[0104] After each round of experimental design sample construction is completed, the newly generated sample points and their corresponding objective response function values ​​should be incorporated into the original sample set to update the input-output pair data used for modeling. The updated sample data should then be used to reconstruct the mathematical expression model corresponding to the current sub-function. Subsequently, the generalization ability of the mathematical expression model should be tested using k-fold cross-validation or leave-one-out cross-validation. During the testing process, the error information between the predicted and actual objective function values ​​should be extracted, and R0 should be calculated respectively. 2 Indices such as RAAE and RMAE are used to evaluate the model's approximation quality and structural stability. Among them:

[0105] Coefficient of determination R 2 The formula for measuring the model's explanatory power for the response trends of sample points is as follows:

[0106]

[0107] Among them, y i Let i be the true target response value of the i-th sample point. These are the model's predicted values. is the mean of all true response values, and n is the total number of samples.

[0108] The relative mean absolute error (RAAE) is used to measure the relative relationship between the model's mean absolute error and the degree of response variability across the entire sample set, and is defined as follows:

[0109]

[0110] Where σ is the true target response value y i Standard deviation, other signs are the same as R 2 Consistent with the above.

[0111] The relative maximum absolute error (RMAE) reflects the maximum error shift that the model may have at local extrema, and is defined as follows:

[0112]

[0113] Similarly, σ is the standard deviation of the true target response value, used to normalize the maximum error magnitude.

[0114] When comparing the extracted error index values ​​with the preset error tolerance threshold, each error index needs to be judged individually. If all error indices meet the preset tolerance range, the mathematical expression model is considered to have stable global fitting ability and local prediction accuracy, and is marked as converged. If at least one error index exceeds the tolerance range, the current model is considered not to have converged, and the experimental design sample expansion operation needs to be performed again to generate new sample points and repeat the above model update and error evaluation process. Through this iterative mechanism, it is ensured that the mathematical expression model of each sub-function achieves stable, convergent, and accurate mapping ability in the local variable space, providing a rigorous foundation for the subsequent construction of the global response model.

[0115] S150, sum all the completed mathematical expression models according to the combination form of the sub-functions to obtain the overall mathematical model of the original second-dimensional ship shape optimization problem.

[0116] In one possible implementation, all the constructed mathematical expression models are summed according to the combination forms corresponding to the sub-functions to obtain the overall mathematical model of the original second-dimensional ship shape optimization problem. Specifically, this includes: structurally combining the mathematical expression models according to the variable dimension hierarchy of the sub-functions, specifically including mathematical expression models of first-order sub-functions, mathematical expression models of second-order sub-functions, and mathematical expression models of multi-order sub-functions, representing the response contributions generated by single-variable influence, bidirectional interaction between variables, and multi-variable coupling effects, respectively; when performing the summation operation, the functional form of each mathematical expression model remains unchanged, and all mathematical expression models use variables that are actually covered in the variable space as independent variables. The superposition process does not introduce dimension misalignment or variable duplication. The overall mathematical model is the algebraic sum of all constructed mathematical expression models.

[0117] Specifically, when structurally combining all mathematical expression models according to the hierarchical dimension of the sub-functions, each completed mathematical expression model should first be classified and organized. Based on the number of variables in its corresponding variable subset, it should be divided into first-order, second-order, and multi-order mathematical expression models. First-order mathematical expression models rely on only a single optimized variable, used to express the independent influence of that variable on the target response function; second-order mathematical expression models rely on two optimized variables, reflecting the combined effect brought about by the bidirectional coupling between variables; multi-order mathematical expression models involve three or more optimized variables, used to characterize the complex response behavior caused by higher-order linkages. This hierarchical structure helps to clarify the dimensional levels of contribution of different variable combinations to the overall response function, ensuring that the response modeling has controllable interpretability and structural clarity.

[0118] When performing the summation operation, the function structure and input dimensions of each mathematical expression model must be strictly maintained. All mathematical expression models should use the optimized variables from their original subsets of variables as input; no additional variables should be introduced or existing variables should be lost. During summation, the mathematical expression models are combined in the form of algebraic summation, i.e., a direct linear superposition of all expression models. To avoid duplicate variable calculations or dimensional misalignment, it must be ensured that each variable participates in modeling only once through its own subset of variables, and that there is no redundant overlap in the variable combinations of all sub-functions within the entire set. This structured algebraic summation process ensures that the mathematical model is logically complete and closed, and its expression is continuous and seamless. The resulting overall mathematical model accurately describes the joint mapping relationship of the original high-dimensional objective response function under all optimized variables, and possesses good structural interpretability, model stability, and numerical analysis characteristics suitable for subsequent optimization solutions. By summing all the constructed mathematical expression models according to the combination forms of their sub-functions, we obtain the overall mathematical model of the original second-dimensional ship shape optimization problem. Its calculation formula can be formally represented as a dimensional decomposition expression of a high-dimensional function, which is essentially a superposition expansion of a high-order response function model. The corresponding general mathematical expression is as follows:

[0119]

[0120] Where, f(x1,x2,…,x) d f represents the final overall mathematical model, i.e., the objective response function obtained by jointly modeling all optimization variables, where f0 is a constant term, usually representing the basic response of all variables to the objective response function at the mean. i (x i f represents the response contribution of the i-th optimization variable acting independently on the objective response function, i.e., the first-order subfunction. ij (x i ,x j ) represents the coupling response contribution between the i-th and j-th optimization variables, i.e., the second-order sub-function, f. ijk (x i ,x j ,x k ) represents a higher-order interactive response among multiple variables, i.e., a third-order or higher-order subfunction, f 1,2,…,d (x1,x2,…,x d ) represents the contribution of the full-order coupling response among all optimization variables, i.e., the highest-order subfunction.

[0121] In one possible implementation, the objective response function of the hull optimization problem is determined and a parametric model of the hull is constructed. The set of optimization variables and the value range of each variable are determined. Specifically, this includes: identifying multiple performance objectives for hull optimization based on the design requirements and operating conditions of a specific ship type; selecting one or more performance objectives that meet preset requirements as optimization objectives, thereby establishing an objective response function for evaluating hull performance; formally expressing the hull geometry using parametric modeling methods, which satisfy requirements such as parameter controllability, hull shape continuity, and consistency of feasible geometric constraints. Specifically, the parametric modeling method maps the hull surface geometry to a finite set of parametric variables, thus forming a parametric expression; after completing the parametric modeling of the hull, determining all optimization variables constituting the set of optimization variables based on the sensitivity of each parameter in the hull optimization design to the objective response function and the actual physical meaning of the variables. These optimization variables include geometric parameters controlling hull line changes and auxiliary structural parameters affecting performance; and setting a value range for each optimization variable, which is comprehensively determined based on design specifications, structural constraints, performance boundaries, and practical engineering experience.

[0122] Specifically, when defining multiple performance objectives for hull optimization, the target vessel's purpose attributes and typical operating conditions should be analyzed first to identify its key performance requirements in hydrodynamics, structural safety, maneuverability, and wave resistance. These requirements may include performance indicators such as minimizing total resistance, optimizing heel stability, minimizing maneuverability delay, minimizing wave loads, and homogenizing structural stress distribution. Based on the design specifications, classification society rules, and risk assessment requirements for typical navigation conditions, a set of multiple performance indicators should be constructed as a preliminary complete set of performance objectives to provide a structured basis for subsequent objective selection and response modeling.

[0123] When selecting one or more performance targets that meet the preset requirements as optimization targets, a performance weight system should be set based on the aforementioned set of performance indicators, combined with multi-objective decision analysis methods (such as the analytic hierarchy process, TOPSIS method, or grey relational analysis). The optimal combination of targets should be determined through normalization processing and comprehensive evaluation calculation. On this basis, a corresponding target response function should be established for each selected optimization target. The response function can be in the form of a physical analytical model, a simulation-based data fitting model, or a hybrid modeling form, ensuring that it has a clear input-output variable relationship and computability for engineering applications.

[0124] When using parametric modeling methods to formally represent the geometry of a ship's hull, a parametric method with local controllability, curvature continuity, and global deformation adjustability should be selected based on the three-dimensional structural division of the hull. Commonly used methods include surface parametric modeling based on Bezier control points, continuous surface modeling based on NURBS structures, or partitioned adjustable methods based on free deformation frames. By introducing control point coordinates, node vectors, or curvature control parameters, the complete hull shape is mapped to a set of finite-dimensional parametric variables, forming a mathematical expression that can be controlled by an optimizer.

[0125] When determining the set of optimization variables based on the sensitivity of each parameter to the target response function and its physical properties, a global sensitivity analysis should first be conducted using sample response data. The independent contribution and interactive influence of each parameter to the target response function should be quantified through Sobol exponent, variance decomposition, or regression coefficient significance assessment, and redundant variables that do not contribute sufficiently to the output should be eliminated. At the same time, the control function and physical meaning of each variable in the hull structure or appendages should be considered, and control variables with key regulatory value should be retained. Finally, an set of optimization variables covering hydrodynamic morphology, appendage structure parameters, and local geometric deformation control parameters should be constructed.

[0126] When setting the range of values ​​for each optimization variable, a comprehensive judgment should be made based on the physical boundary characteristics of the variable, engineering manufacturing limitations, structural strength and safety specifications, and empirical statistical data. First, theoretical upper and lower limits should be set, and then the range should be narrowed based on historical design cases and performance evaluation boundary conditions. The possible coupling or constraint relationships between variables should also be considered. By introducing linear inequality constraints or nonlinear boundary expressions, an optimization variable value space containing upper and lower bound constraints and variable linkage restrictions should be constructed to provide a strict and effective parameter control basis for modeling, solving, and optimization execution.

[0127] This embodiment also discloses a device for constructing a high-dimensional approximate model in ship morphology optimization, referring to... Figure 2 The device includes an acquisition module 201, a processing module 202, and an output module 203. It is used to execute any of the methods described above for constructing a high-dimensional approximation model in ship morphology optimization, wherein:

[0128] The acquisition module 201 is used to determine the objective response function of the ship type optimization problem and construct the ship type parameterized model, and to determine the set of optimization variables used for ship type optimization and the value range of each variable.

[0129] The processing module 202 is used to decompose the set of optimization variables according to the coupling relationship between the optimization variables, obtain several sub-variable combinations, and construct multiple sub-functions according to the number of variables contained in each sub-variable combination, so as to represent the independent or coupled influence of different variable combinations on the output value of the target response function.

[0130] The processing module 202 is used to select sample points in the corresponding variable space based on the experimental design method for each sub-problem corresponding to the sub-function, and construct the mathematical expression model of the first dimension of the sub-problem.

[0131] The processing module 202 is used to continuously determine whether each mathematical expression model has reached the convergence standard during the construction process by using the convergence judgment criterion. If it has not converged, it continues to iterate and update the mathematical expression model until the convergence criterion is met.

[0132] Output module 203 is used to sum all the completed mathematical expression models according to the combination form of the sub-functions to obtain the overall mathematical model of the original second-dimensional ship shape optimization problem, where the first dimension is lower than the second dimension.

[0133] In one possible implementation, the processing module 202 is used to define multiple performance objectives for hull optimization based on the design requirements and operating conditions of a specific ship type.

[0134] The acquisition module 201 is used to select one or more performance targets that meet the preset requirements from multiple performance targets as optimization targets, thereby establishing a target response function for evaluating ship performance.

[0135] The processing module 202 is used to formally express the hull geometry using a parametric modeling method. The parametric modeling method satisfies requirements such as parameter controllability, hull shape continuity, and consistency of feasible geometric constraints. Specifically, the parametric modeling method maps the hull surface geometry to a set of finite parametric variables, thereby forming a parametric expression.

[0136] The processing module 202 is used to determine all optimization variables that constitute the set of optimization variables after the parametric modeling of the hull is completed, based on the sensitivity of each parameter in the hull optimization design to the target response function and the actual physical meaning of the variables. The optimization variables include geometric parameters that control the change of hull lines and auxiliary structural parameters that affect performance.

[0137] The processing module 202 is used to set the value range for each optimization variable. The value range is determined comprehensively based on design specifications, structural constraints, performance boundaries and actual engineering experience.

[0138] In one possible implementation, the acquisition module 201 is used to select multiple test functions with different numbers of variables and complex coupling relationships as evaluation benchmarks. The response functions of the test functions have known analytical expressions and have different degrees of variable interaction characteristics in structure, so as to form a test set covering various response behaviors such as single variable dominance, multivariate coupling, and local extremum complexity.

[0139] The acquisition module 201 is used to construct a mathematical model for each test function to obtain the test mathematical model.

[0140] Processing module 202 is used to evaluate each test mathematical model using a uniformly sampled test sample set after the test mathematical model is constructed. The evaluation index includes the coefficient of determination R. 2 The relative mean absolute error (RAAE) and the relative maximum absolute error (RMAE) are also considered.

[0141] In one possible implementation, the processing module 202 is used to systematically analyze all optimization variables by means of identifying the interrelationships between optimization variables, so as to identify the interaction relationships between each optimization variable in the target response function. In this process, a preliminary sample response dataset of the target response function with respect to all optimization variables is constructed, and based on the preliminary sample response dataset, the marginal impact of each optimization variable on the target response function when other optimization variables remain constant is analyzed, as well as the trend of the combined response change of the target response function when multiple optimization variables change in tandem, to determine whether there is an interaction effect between optimization variables. If there is an interaction effect, the multiple optimization variables are classified as a combination of coupled variables.

[0142] The processing module 202 is used to decompose the set of optimization variables into several variable subsets based on the identification results of the combination of coupled variables. Each variable subset consists of a set of optimization variables with interaction, and ensures that each optimization variable belongs to at least one variable subset.

[0143] The processing module 202 is used to classify all variable subsets into one-variable subsets, two-variable subsets, and multi-variable subsets according to the number of optimization variables contained in the variable subsets, and construct first-order sub-functions, second-order sub-functions, and multi-order sub-functions accordingly. Each sub-function serves as a local response mapping of the target response function under the corresponding variable subset.

[0144] In one possible implementation, the processing module 202 is used to define the input domain of the sub-function corresponding to each subset of variables, for each subset of variables that has been divided, the variable space being the parameter domain spanned by all the optimized variables in the subset of variables.

[0145] Processing module 202 is used to select an experimental design method to generate a sample point set based on the structural characteristics of the variable space and the dimension of the sub-functions.

[0146] The processing module 202 is used to generate a set of sample points in the variable space using the selected experimental design method, and to calculate or simulate the target response function value of the sub-function at each sample point in the sample point set, thereby forming an input-output pair of the sample points.

[0147] Processing module 202 is used to construct a mathematical expression model of a sub-function based on multiple input-output pairs. The mathematical expression model expresses the input-output mapping relationship of the sub-function in the variable space. According to the mathematical expression model, the dimension of the input variables is limited to the optimized variables in the variable subset.

[0148] In one possible implementation, the processing module 202 is used to set a convergence criterion for the mathematical expression model corresponding to each sub-function. The convergence criterion is used to evaluate the degree to which the mathematical expression model approximates the target response function in the variable space.

[0149] The processing module 202 is used to update the mathematical expression model with the new experimental design sample and the corresponding target response value after each round of experimental design sample construction is completed, and to perform cross-validation on the updated mathematical expression model and extract the error index value.

[0150] The processing module 202 is used to compare the error index value with the preset error tolerance threshold. If the error index value is within the error tolerance threshold, it is determined that the mathematical expression model has converged.

[0151] In one possible implementation, the processing module 202 is used to structurally combine the mathematical expression models according to the variable dimension hierarchy of the sub-functions, specifically including the mathematical expression models of first-order sub-functions, second-order sub-functions, and multi-order sub-functions, which respectively represent the response contributions generated by the influence of a single variable, the bidirectional interaction between variables, and the coupling effect of multiple variables.

[0152] The processing module 202 is used to maintain the functional form of each mathematical expression model unchanged when performing the summation operation, and all mathematical expression models take the variables that are actually covered in the variable space as independent variables. The superposition process does not introduce dimensional misalignment or repeated calculation of variables, and the overall mathematical model is the algebraic sum of all constructed mathematical expression models.

[0153] It should be noted that the above embodiments of the apparatus are only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the apparatus and method embodiments provided in the above embodiments belong to the same concept, and the specific implementation process can be found in the method embodiments, which will not be repeated here.

[0154] This embodiment also discloses an electronic device, as shown in the reference. Figure 3 The electronic device may include: at least one processor 301, at least one communication bus 302, user interface 303, network interface 304, and at least one memory 305.

[0155] The communication bus 302 is used to enable communication between these components.

[0156] The user interface 303 may include a display screen and a camera. Optionally, the user interface 303 may also include a standard wired interface and a wireless interface.

[0157] The network interface 304 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0158] The processor 301 may include one or more processing cores. The processor 301 connects to various parts of the server using various interfaces and lines, and performs various server functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in the memory 305, and by calling data stored in the memory 305. Optionally, the processor 301 may be implemented using at least one hardware form of Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), or Programmable Logic Array (PLA). The processor 301 may integrate one or a combination of several of the following: Central Processing Unit (CPU), Graphics Processing Unit (GPU), and modem. The CPU primarily handles the operating system, user interface, and applications; the GPU is responsible for rendering and drawing the content required for display; and the modem handles wireless communication. It is understood that the modem may also not be integrated into the processor 301 and may be implemented as a separate chip.

[0159] The memory 305 may include random access memory (RAM) or read-only memory. Optionally, the memory may include a non-transitory computer-readable storage medium. The memory 305 may be used to store instructions, programs, code, code sets, or instruction sets. The memory 305 may include a program storage area and a data storage area. The program storage area may store instructions for implementing an operating system, instructions for at least one function (such as touch functionality, sound playback functionality, image playback functionality, etc.), instructions for implementing the various method embodiments described above, etc.; the data storage area may store data involved in the various method embodiments described above, etc. Optionally, the memory 305 may also be at least one storage device located remotely from the aforementioned processor 301. As a computer storage medium, the memory 305 may include an operating system, a network communication module, a user interface 303 module, and an application program for constructing a high-dimensional approximation model in ship hull optimization.

[0160] exist Figure 3 In the electronic device shown, the user interface 303 is mainly used to provide an input interface for the user and obtain the user input data; while the processor 301 can be used to call the application program stored in the memory 305 that stores a method for constructing a high-dimensional approximation model in ship hull optimization. When executed by one or more processors 301, the electronic device executes one or more methods as described in the above embodiments.

[0161] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0162] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0163] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the shown or discussed mutual couplings or direct couplings or communication connections may be through some service interfaces; indirect couplings or communication connections between apparatuses or units may be electrical or other forms.

[0164] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0165] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0166] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory 305 and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned memory 305 includes various media capable of storing program code, such as a USB flash drive, external hard drive, magnetic disk, or optical disk.

[0167] This application also discloses a computer-readable storage medium storing instructions. When executed by one or more processors 301, these instructions cause an electronic device to perform one or more methods as described in the above embodiments.

[0168] The above are merely exemplary embodiments of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of other embodiments of this disclosure upon considering the specification and the disclosure of practical truth. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A method for constructing a high-dimensional approximate model in ship hull optimization, characterized in that, The method includes: Determine the objective response function of the ship morphology optimization problem and construct a parametric model of the ship morphology, and determine the set of optimization variables used for ship morphology optimization and the range of values ​​for each variable; Based on the coupling relationship between the optimization variables, the set of optimization variables is decomposed to obtain several sub-variable combinations. Based on the number of variables contained in each sub-variable combination, multiple sub-functions are constructed to represent the independent or coupled effects of different variable combinations on the output value of the target response function. For each sub-problem corresponding to the sub-function, sample points are selected in the corresponding variable space based on the experimental design method to construct the mathematical expression model of the first dimension of the sub-problem; During the construction process, the convergence judgment criterion is used to continuously determine whether each mathematical expression model has reached the convergence standard. If it has not converged, the mathematical expression model is iteratively updated until the convergence criterion is met. All the constructed mathematical expression models are summed according to the combination form corresponding to the sub-functions to obtain the overall mathematical model of the original second-dimensional ship shape optimization problem, wherein the first dimension is lower than the second dimension; Based on the coupling relationships between the optimization variables, the set of optimization variables is decomposed to obtain several combinations of sub-variables. Then, based on the number of variables in each sub-variable combination, multiple sub-functions are constructed to represent the independent or coupled effects of different variable combinations on the output value of the target response function. Specifically, this includes: By using the methods for identifying the interrelationships between the optimization variables, a systematic analysis is performed on all the optimization variables to identify the interaction relationships between each optimization variable in the target response function. Specifically, a preliminary sample response dataset of the target response function with respect to all the optimization variables is constructed, and based on the preliminary sample response dataset, the marginal impact of each optimization variable on the target response function when other optimization variables remain constant is analyzed, as well as the trend of combined response changes to the target response function when multiple optimization variables change in tandem. It is determined whether there is an interaction effect between the optimization variables. If the interaction effect exists, multiple optimization variables are classified as a combination of coupled variables. Based on the identification results of the coupling variable combination, the set of optimization variables is decomposed into several variable subsets. Each variable subset consists of a set of optimization variables with interactive effects, and it is ensured that each optimization variable belongs to at least one of the variable subsets. Next, according to the number of optimization variables contained in the variable subset, all the variable subsets are classified into one-variable subsets, two-variable subsets, and multi-variable subsets, and corresponding first-order sub-functions, second-order sub-functions, and multi-order sub-functions are constructed. Each sub-function serves as a local response mapping of the target response function under the corresponding variable subset.

2. The method for constructing a high-dimensional approximate model in ship morphology optimization according to claim 1, characterized in that, The process of determining the objective response function for the ship morphology optimization problem and constructing a parametric model of the ship morphology, as well as determining the set of optimization variables used for ship morphology optimization and the value range of each variable, specifically includes: Based on the design requirements and operating conditions of specific ship types, multiple performance objectives for hull optimization are defined. One or more performance targets that meet the preset requirements are selected from the multiple performance targets as optimization targets, thereby establishing a target response function for evaluating ship performance; A parametric modeling method is used to formally represent the hull geometry. The parametric modeling method satisfies the requirements of parameter controllability, hull shape continuity, and consistency of feasible geometric constraints. The parametric modeling method maps the hull surface geometry to a set of finite parametric variables, thereby forming a parametric expression. After completing the parametric modeling of the hull, based on the sensitivity of each parameter in the hull optimization design to the target response function and the actual physical meaning of the variables, all optimization variables constituting the set of optimization variables are determined. The optimization variables include geometric parameters that control the changes in hull lines and auxiliary structural parameters that affect performance. A range of values ​​is set for each of the optimization variables, and the range of values ​​is determined comprehensively based on design specifications, structural constraints, performance boundaries and practical engineering experience.

3. The method for constructing a high-dimensional approximate model in ship morphology optimization according to claim 1, characterized in that, After summing all the constructed mathematical expression models according to the combination forms corresponding to the sub-functions to obtain the overall mathematical model of the original second-dimensional ship shape optimization problem, the method further includes: Multiple test functions with different numbers of variables and complex coupling relationships are selected as evaluation benchmarks. The response functions of the test functions have known analytical expressions and have different degrees of variable interaction characteristics in structure, so as to form a test set covering various response behaviors such as single variable dominance, multivariate coupling, and local extremum complexity. For each of the test functions, a mathematical model is constructed to obtain the test mathematical model; After the test mathematical model is constructed, each test mathematical model is evaluated using a uniformly sampled test sample set. The evaluation metrics include the coefficient of determination R², the relative mean absolute error RAAE, and the relative maximum absolute error RMAE.

4. The method for constructing a high-dimensional approximate model in ship morphology optimization according to claim 1, characterized in that, For each sub-function corresponding to a sub-problem, sample points are selected in the corresponding variable space based on the experimental design method to construct a mathematical expression model of the first dimension of the sub-problem, specifically including: For each of the defined variable subsets, the variable space is defined as a parameter domain spanned by all the optimized variables in the variable subsets, and the input domain of the sub-functions corresponding to the variable subsets is defined. Based on the structural characteristics of the variable space and the dimension of the sub-function, an experimental design method is selected to generate the sample point set; The sample point set is generated within the variable space using the selected experimental design method, and the target response function value of the sub-function at the sample point is calculated or simulated for each sample point in the sample point set, thereby forming the input-output pair of the sample points; Based on multiple input-output pairs, a mathematical expression model of the sub-function is constructed. The mathematical expression model expresses the input-output mapping relationship of the sub-function in the variable space. According to the mathematical expression model, the dimension of the input variables is limited to the optimized variables in the variable subset.

5. The method for constructing a high-dimensional approximate model in ship morphology optimization according to claim 1, characterized in that, During the construction process, a convergence criterion is used to continuously determine whether each mathematical expression model has reached the convergence standard. If convergence is not achieved, the mathematical expression model is iteratively updated until the convergence criterion is met. Specifically, this includes: A convergence criterion is set for the mathematical expression model corresponding to each sub-function. The convergence criterion is used to evaluate the degree of approximation of the mathematical expression model to the target response function in the variable space. After each round of experimental design samples is constructed, the mathematical expression model is updated using the new experimental design samples and the corresponding target response values, and the updated mathematical expression model is cross-validated to extract the error index value. The error index value is compared with a preset error tolerance threshold. If the error index value is within the error tolerance threshold, the mathematical expression model is determined to have converged.

6. The method for constructing a high-dimensional approximate model in ship morphology optimization according to claim 1, characterized in that, The step involves summing all the constructed mathematical expression models according to the combination forms corresponding to the sub-functions to obtain the overall mathematical model of the original second-dimensional ship shape optimization problem, specifically including: The mathematical expression models are structurally combined according to the variable dimension hierarchy of the sub-functions, specifically including the mathematical expression models of the first-order sub-functions, the second-order sub-functions, and the multi-order sub-functions, which respectively represent the response contributions generated by the influence of a single variable, the bidirectional interaction between variables, and the multivariate coupling effect. When performing the summation operation, the functional form of each of the mathematical expression models remains unchanged, and all the mathematical expression models take the variables that are actually covered in the variable space as independent variables. The superposition process does not introduce dimensional misalignment or repeated calculation of variables. The overall mathematical model is the algebraic sum of all the constructed mathematical expression models.

7. A device for constructing a high-dimensional approximate model in ship hull optimization, characterized in that, The apparatus is used to execute a method for constructing a high-dimensional approximate model in ship morphology optimization as described in any one of claims 1-6. The apparatus includes an acquisition module (201), a processing module (202), and an output module (203), wherein: The acquisition module (201) is used to determine the objective response function of the ship type optimization problem and construct a ship type parameterized model, and to determine the set of optimization variables for ship type optimization and the value range of each variable; The processing module (202) is used to decompose the set of optimization variables according to the coupling relationship between the optimization variables to obtain several sub-variable combinations, and to construct multiple sub-functions according to the number of variables contained in each sub-variable combination, so as to represent the independent or coupled influence of different variable combinations on the output value of the target response function. The processing module (202) is used to select sample points in the corresponding variable space based on the experimental design method for each sub-problem corresponding to the sub-function, and construct a mathematical expression model of the first dimension of the sub-problem; The processing module (202) is used to continuously determine whether each mathematical expression model has reached the convergence standard during the construction process by using the convergence judgment criterion. If it has not converged, it continues to iteratively update the mathematical expression model until the convergence criterion is met. The output module (203) is used to sum all the completed mathematical expression models according to the combination form corresponding to the sub-functions to obtain the overall mathematical model of the original second-dimensional ship shape optimization problem, wherein the first dimension is lower than the second dimension.

8. An electronic device, characterized in that, The device includes a processor (301), a communication bus (302), a user interface (303), a network interface (304), and a memory (305). The memory (305) is used to store instructions. The user interface (303) and the network interface (304) are both used to communicate with other devices. The communication bus (302) is used to realize the connection and communication between the components within the electronic device. The processor (301) is used to execute the instructions stored in the memory (305) so that the electronic device performs the method as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed, perform the method as described in any one of claims 1-6.

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