Response surface method-based offshore structure pipe node lightweight design method and system

Abstract

The invention belongs to the technical field of offshore converter station construction design, and provides an offshore structural pipe node lightweight design method and system based on a response surface method.The method comprises the steps that a target function is established with the minimum total weight of structural pipe nodes as the target and the condition that the ultimate strength stress ratio is not larger than a preset allowable value as the constraint condition; adopting Latin hypercube sampling to generate a series of test sample points; extracting a structure response value corresponding to each sample point; according to the structure response value, a response surface method is adopted for fitting to obtain a polynomial function; obtaining a lightweight design scheme according to the polynomial function; according to the method, a stress ratio response surface in a high-dimensional design space can be effectively fitted based on a sampled high-precision response surface model, collaborative optimization is carried out on a plurality of key design parameters of a complex pipe node on the premise of meeting safety specifications, constraint conditions of different diagonal bracings are met, structural redundancy can be accurately released, and the design efficiency is improved. And obvious weight reduction is realized on the basis of not sacrificing safety.

Description

Technical Field

[0001] This invention belongs to the field of construction and design technology of offshore converter stations, and in particular relates to a lightweight design method and system for offshore structural pipe nodes based on response surface methodology. Background Technology

[0002] In marine structures, complex pipe joints are key force-transmitting units connecting various members, consisting of multiple pipes of different diameters and orientations converging in the same area. Multiple intersecting lines approach or even cross each other on the surface of the main pipe, resulting in dense and interlaced welds, forming highly complex spatial curves, leading to complex multiaxial stress states and multiple high-stress zones.

[0003] For complex pipe joints connecting columns to multiple diagonal braces and beams, designers typically adopt a conservative approach, such as increasing the wall thickness of the components, to ensure sufficient safety margins for the joints. However, while this overly conservative design ensures safety, it also results in significant strength redundancy at the joints. For example, the total weight of the steel structure of a large offshore platform's superstructure can reach tens of thousands of tons, and any local structural overweight will accumulate into a significant economic burden. Summary of the Invention

[0004] To address the aforementioned problems, this invention proposes a lightweight design method and system for marine structural pipe nodes based on the response surface methodology. This invention utilizes a high-precision response surface model based on sampling, which can effectively fit the stress ratio response surface in a high-dimensional design space. While meeting safety standards, it collaboratively optimizes multiple key design parameters of complex pipe nodes, satisfying the constraints of different bracing elements while precisely releasing structural redundancy. This achieves significant weight reduction without sacrificing safety, thereby resolving the contradiction between safety, economy, and efficiency in current designs.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution: In a first aspect, the present invention provides a lightweight design method for marine structural pipe nodes based on the response surface methodology, comprising: Establish a parameterized 3D solid model of the target pipe node; with the goal of minimizing the total weight of the structural pipe node and the constraint that the ultimate strength stress ratio is not greater than the preset allowable value, establish an objective function; Based on the three-dimensional solid model and the objective function, a series of experimental sample points are generated using Latin hypercube sampling. Extract the structural response value corresponding to each sample point; Based on the structural response values, a polynomial function is obtained by fitting using the response surface methodology. Based on the polynomial function, a lightweight design scheme is obtained.

[0006] Furthermore, when determining the constraints, the strength check stress ratio at all connection welds must meet the allowable stress ratio limit; the constraints also include geometric dimensions.

[0007] Furthermore, when generating samples using Latin hypercube sampling, the constraint is that the wall thickness of the main pipe is greater than that of the branch pipe, ensuring that the combination of sample points conforms to mechanical constraints.

[0008] Furthermore, for each sample point combination, structural analysis is performed using numerical simulation methods. First, an overall platform model is established to extract the axial force, shear force, and bending moment of the adjacent sections of the target node. Then, a solid sub-model is established, and based on the rule that the node load is along the global coordinate and the member load is along the local coordinate, the internal force data is applied as boundary loads and analyzed to finally obtain the accurate stress ratio.

[0009] Furthermore, the fitted polynomial function is: ; in, It is the structural response value predicted by the model; and These are design variables; These are the undetermined coefficients obtained through regression analysis.

[0010] Furthermore, based on the polynomial function, objective function, and constraints, a sequential quadratic programming algorithm is used to solve the problem, resulting in a combination of design variables that minimizes the total weight of the structure while satisfying all stress ratios and other constraints.

[0011] Secondly, the present invention also provides a lightweight design system for marine structural pipe nodes based on the response surface methodology, comprising: The objective function creation module is configured to: create a parameterized 3D solid model of the target pipe node; and create an objective function with the goal of minimizing the total weight of the structural pipe node and the constraint that the ultimate strength stress ratio is not greater than a preset allowable value. The sample point generation module is configured to generate a series of test sample points based on the 3D solid model and the objective function using Latin hypercube sampling. The response value extraction module is configured to extract the structural response value corresponding to each sample point. The polynomial function creation module is configured to: obtain a polynomial function by fitting the response surface method based on the structural response value; The design module is configured to: obtain a lightweight design scheme based on a polynomial function.

[0012] Thirdly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the lightweight design method for marine structural pipe nodes based on the response surface methodology described in the first aspect.

[0013] Fourthly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the program to implement the steps of the lightweight design method for marine structural pipe nodes based on the response surface methodology described in the first aspect.

[0014] Fifthly, the present invention also provides a computer program product, the computer program product comprising a computer program, which, when executed by a processor, implements the steps of the lightweight design method for marine structural pipe nodes based on the response surface methodology described in the first aspect.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention aims to minimize the total weight of structural pipe nodes, with the constraint that the ultimate strength stress ratio does not exceed a preset allowable value, and establishes an objective function. Latin hypercube sampling is used to generate a series of test sample points; the structural response value corresponding to each sample point is extracted; based on the structural response value, a polynomial function is obtained by fitting using the response surface methodology; and a lightweight design scheme is derived based on the polynomial function. This invention, based on a high-precision response surface model using sampling, can effectively fit the stress ratio response surface in a high-dimensional design space. Under the premise of meeting safety specifications, it collaboratively optimizes multiple key design parameters of complex pipe nodes, satisfying the constraints of different bracing elements while accurately releasing structural redundancy. This achieves significant weight reduction without sacrificing safety, thereby resolving the contradiction between safety, economy, and efficiency in current designs.

[0016] 2. This invention directly constructs the stress ratio response surface, replacing the traditional method of predicting stress or displacement, omitting the result transformation step and directly outputting compliant dimensions, which greatly improves the efficiency of design iteration; at the same time, it sets the standard limit as a direct constraint, avoiding complex manual judgment, realizing the precise connection between the optimization process and engineering specifications, and ensuring that the solution is compliant and reliable.

[0017] 3. This invention overcomes the limitations of traditional trial-and-error methods by employing systematic multi-parameter collaborative optimization. This method fully considers the coupling effects between various design variables to find the global optimal solution, and ensures high reliability of the results through final verification. By replacing high-cost simulation analysis with a highly efficient surrogate model, the optimization calculation time, which used to take weeks or even months, is shortened to days, greatly improving the speed of design iteration and significantly reducing the product development cycle. By using safety constraints as rigid boundaries for optimization and setting up a dual verification mechanism of "surrogate model optimization – original model verification," the contradiction between safety and economy is successfully resolved, providing a safe, reliable, and economically efficient advanced technical approach. Attached Figure Description

[0018] The accompanying drawings, which form part of this embodiment, are used to provide a further understanding of this embodiment. The illustrative embodiments and their descriptions are used to explain this embodiment and do not constitute an improper limitation of this embodiment.

[0019] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the node locations and the names of each node in Embodiment 2 of the present invention; Figure 3 This is a residual analysis diagram of the fitting of the response surface model of the inclined support 1 in Embodiment 2 of the present invention—a residual diagram; Figure 4 This is a fitting residual analysis diagram—a normal probability diagram—of the response surface model of the inclined support 1 in Embodiment 2 of the present invention. Figure 5 The residual distribution is shown in the fitting residual analysis diagram of the response surface model of the inclined support 1 in Embodiment 2 of the present invention. Among them, 2131 is the pipe node; 3102 is the first connecting pipe; 3103 is the second connecting pipe; 3036 is the third connecting pipe; 3045 is the fourth connecting pipe; and 3054 is the fifth connecting pipe. Detailed Implementation

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0022] Example 1: Large offshore converter stations and other typical marine engineering platforms are subjected to extreme marine environmental loads such as wind, waves, and currents year-round, making structural safety and reliability the primary design consideration. Complex pipe joints in offshore structures are key force-transmitting units connecting various members, consisting of multiple pipes of different diameters and orientations converging in the same area. Multiple intersecting lines approach or even cross each other on the main pipe surface, resulting in dense, interlaced welds and forming highly complex spatial curves, leading to complex multiaxial stress states and multiple high-stress zones. This extremely high stress concentration makes them highly sensitive to fatigue; therefore, the safety design of pipe joints is particularly important.

[0023] In current engineering practice, designers often adopt a conservative approach for complex pipe joints connecting columns to multiple diagonal braces and beams, such as increasing the wall thickness of the components to ensure sufficient safety margins. However, while this overly conservative design ensures safety, it also leads to significant strength redundancy in the joints. Taking large offshore platforms as an example, the total weight of the steel structure of their superstructure can reach tens of thousands of tons, and any local structural overweight will accumulate into a significant economic burden.

[0024] Based on the above problems, this embodiment provides a lightweight design method for marine structural pipe nodes based on the response surface methodology. It innovatively selects the stress ratio as the core constraint response for the lightweight design of complex pipe nodes in marine structures, aiming to eliminate strength redundancy in a targeted manner while ensuring structural safety, thereby achieving structural lightweighting.

[0025] Although the industry has attempted to design lightweight structures, there are significant limitations. In traditional optimization, reducing the outer diameter of a brace may increase its stress ratio (UC) value and may also significantly affect the UC values ​​of adjacent braces due to changes in overall stiffness, thereby compromising structural safety. For complex pipe nodes with multiple braces, it is difficult to find the global optimal solution through traditional manual trial and error or local optimization methods. At the same time, traditional surrogate models (such as those using only first- or second-order polynomials) are difficult to accurately capture such local nonlinear responses and involve a large amount of computation.

[0026] The high-precision response surface model based on LHS sampling used in this embodiment can effectively fit the stress ratio (UC) response surface in the high-dimensional design space. Under the premise of strictly meeting all safety specifications, it can collaboratively optimize multiple key design parameters of complex pipe nodes, which can satisfy the constraints of different bracing and accurately release structural redundancy. It can achieve significant weight reduction without sacrificing safety, thereby resolving the contradiction between safety, economy and efficiency in the current design.

[0027] Compared to common planar T-shaped, K-shaped, or cross-shaped nodes, this embodiment focuses on spatial nodes, which are a type of critical node in large offshore platforms that bear more complex loads and face more severe stress conditions. These nodes are characterized by high-dimensional coupling, interlaced stress concentration zones, and high model accuracy requirements.

[0028] Complex pipe nodes with multiple diagonal braces involve multiple components whose parameters interact spatially, forming a high-dimensional design space. Even a slight adjustment to any single parameter can trigger a chain reaction in the stress ratio at other diagonal brace connections.

[0029] The design method in this embodiment combines parametric modeling, Latin hypercube sampling, response surface methodology, and an optimization solution system to address the technical problems in existing design methods where excessive conservatism leads to significant structural redundancy, resulting in excessive structural weight, material waste, and high manufacturing costs and engineering risks. This embodiment aims to minimize the weight of the pipe node structure while strictly meeting structural strength and safety specifications. Figure 1 As shown, the optimization method specifically includes the following steps: S1. Describe the optimization problem mathematically and establish a parameterized optimization model (three-dimensional solid model) that includes the optimization objective and constraints.

[0030] S1.1 Establish the objective function: The objective function is to minimize the total structural weight, with the core constraint being that the structural response (e.g., the ultimate strength stress ratio) must be less than or equal to a preset allowable value. The objective function is a nonlinear, high-dimensional function with respect to multiple design variables. It reflects the total weight of the tubular structure that affects the strength of the node, embodying the design goal of optimizing and lightweighting the node.

[0031] Allowable values ​​are typically determined based on relevant design specifications, with a certain safety margin considered, such as taking 80% of the specification limit. The model also includes other necessary design constraints such as the minimum outer diameter of the component and manufacturing process. It can be expressed by the following formula: ; in, This represents the total weight of the node. These are key design variables defined in subsequent steps.

[0032] S1.2 Determine the constraints: To ensure the absolute safety of the optimized structure, this embodiment sets strict multiple constraints. Complex pipe joints have multiple high-stress zones, therefore the constraints must be "multiple constraints." That is, under all preset extreme load combinations, the strength check stress ratio at all critical connection welds must meet the allowable stress ratio limit, thereby avoiding the limitation of traditional designs that only focus on a few stress concentration points.

[0033] First, there is the ultimate strength constraint, which requires that under all preset extreme load combinations, the strength check stress ratio at each connection weld of the node must meet the following requirements: ; in, For the first i Stress ratio at key locations; This is the allowable stress ratio limit. For the allowable value... Based on the safety factor adopted by the platform specifications under the preset extreme load conditions, the specification limit can be quantified to avoid the problem of uncontrollable safety margin and excessive redundancy, thus achieving precise control to release redundancy to the maximum extent while meeting safety requirements.

[0034] Secondly, there are other geometric or technological constraints that require all design variables to take values ​​within a reasonable range that meets manufacturing process requirements: ; in, It is the first i The geometric dimensions of each design variable, and These are the minimum and maximum values ​​allowed for the design variable, respectively, and these boundaries are determined by manufacturing processes, specification requirements, or other geometric constraints.

[0035] S2. Identify the key geometric parameters that affect structural performance as design variables.

[0036] Clearly define the design variable vector in the optimization model of step S1. The specific physical parameters. This identification process is based on the analysis of the force transmission path of the structure, engineering experience, or preliminary parameter sensitivity studies, and aims to screen out a set of geometric dimensions that have the most significant impact on the total weight of the structure (optimization objective) and mechanical performance (constraints).

[0037] For the complex pipe joint structure addressed in this embodiment, these key design variables typically include the outer diameter of the main pipe and the outer diameters of each branch pipe. Ultimately, these selected n physical parameters are defined as the design variables to be optimized. This forms the basis for solving optimization problems.

[0038] S3. Generate sample combinations through experimental design and use numerical simulation to calculate the corresponding structural response data.

[0039] S3.1, Generate test sample points: Within the geometric and technological constraint boundaries defined by step S1 Within the multidimensional design space, a series of experimental sample points are generated using Design of Experiments (DoE) methods, such as Latin Hypercube Sampling (LHS).

[0040] In addition to setting dimensional constraints such as minimum outer diameter, geometric validity or force transmission order constraints also need to be added to prevent unreasonable dimensions from causing force transmission disorder or modeling failure during numerical simulation. Specifically, the main pipe wall thickness should be greater than the branch pipe wall thickness to meet the minimum stiffness ratio requirement and ensure a reasonable force transmission path. When generating samples using Latin hypercube sampling, these geometric constraints are used as pre-filtering conditions to ensure that the combination of sample points conforms to mechanical constraints, thereby ensuring stable and accurate convergence of the numerical simulation, reflecting the actual structural force transmission characteristics, and avoiding force transmission disorder.

[0041] S3.2 Calculate the structural response value: For each generated combination of sample points, i.e. a specific set of sample points A complete structural analysis is performed using numerical simulation methods. This analysis process is typically implemented using specialized structural simulation software, such as SACS software in the field of marine engineering.

[0042] The numerical simulation employs a global-to-local sub-model technique. For complex pipe nodes, a global platform model is first established using software such as SACS and analyzed under extreme conditions to ensure accurate macroscopic response. Then, internal force data, including axial force, shear force, and bending moment, are extracted from adjacent sections of the target node. Subsequently, a solid sub-model is established, and based on the rule that node loads are along global coordinates and member loads are along local coordinates, the internal force data are applied as boundary loads and analyzed to ultimately obtain an accurate stress ratio.

[0043] This analysis calculates and extracts the structural response value corresponding to each sample point, specifically including the optimization target value defined in step S1, i.e., the total structural weight. And the response values ​​in all constraints, i.e., the stress ratios at each critical location. .

[0044] Finally, the output of step S3 is a structured database. Each record contains a set of input design variables. and its corresponding output response value obtained through precise calculation. and This database will serve as the direct input for model fitting in step S4.

[0045] The choice of this method ensures the uniformity and representativeness of the sample points throughout the design space, avoids data aggregation, and lays a solid data foundation for building a globally accurate surrogate model.

[0046] Step S3 aims to generate a set of high-quality "design variable-structural response" data for the proxy model construction in the subsequent step S4.

[0047] S4. Based on sample data, use response surface methodology to construct an explicit proxy model that can replace numerical simulation.

[0048] Step S4 aims to address the problems of high computational cost and excessive time consumption in the numerical simulation process of step S3. Its core task is to establish a set of explicit mathematical models that can accurately replace the numerical simulation process, i.e., surrogate models or response surface models.

[0049] The main technique used in step S4 is the Response Surface Methodology (RSM). Specifically, this step utilizes the "design variable-structural response" database generated in step S3. By applying statistical regression analysis to this database, a pre-defined polynomial function is fitted to determine the unknown coefficients in the function. .

[0050] This process requires building an independent response surface model for each structural response. Ultimately, this will generate a model tailored to the optimization objective. The model, and a set of constraints respectively. The model.

[0051] The general mathematical form of these response surface models can be expressed as: ; in, These are structural response values ​​predicted by the model, such as total weight or stress ratio at a certain location; and These are design variables; These are the undetermined coefficients obtained through regression analysis.

[0052] S5. Combine the surrogate model and optimization algorithm to find the optimal design scheme and perform final verification.

[0053] Step S5 aims to solve the explicit mathematical problem constructed in step S4 and rigorously verify the obtained solution to obtain a final, reliable lightweight design scheme. This step includes the following steps: S5.1. Combine the multiple response surface models for weight and stress ratio established in step S4 with the objective function and constraints defined in step S1 to form a complete, explicit optimization problem. Then, apply mature mathematical optimization algorithms, such as sequential quadratic programming or multi-objective genetic algorithms, to solve this explicit problem. This algorithm can systematically explore the entire design space in a very short time and efficiently identify factors that minimize the total structural weight. The minimum combination of design variables that simultaneously satisfies all stress ratios and other constraints. This combination is called the candidate optimal solution.

[0054] S5.2 To ensure the absolute safety and accuracy of the final solution, the candidate optimal solutions obtained through the optimization algorithm cannot be directly adopted and must undergo a final verification process. This verification involves verifying the candidate optimal solutions... The specific set of geometric dimensions represented are then re-entered into the high-fidelity structural simulation analysis software used in step S3, such as SACS, for an independent and complete numerical simulation verification.

[0055] S5.3. The candidate optimal solution satisfies all design constraints in the original simulation model if and only if the results of high-fidelity verification show that the maximum stress ratio is still lower than the allowable value. This set of design variables It was then confirmed as the final lightweight design solution.

[0056] Compared with existing technologies, this embodiment integrates parametric modeling, experimental design, response surface methodology, and optimization algorithms, forming a complete systematic design process, thereby achieving the following beneficial effects: This embodiment, while strictly meeting safety standards, precisely eliminates structural redundancy through global optimization, significantly reducing overall costs such as materials, manufacturing, and shipping, resulting in substantial economic benefits.

[0057] This embodiment directly constructs the stress ratio response surface, replacing the traditional method of predicting stress or displacement, omitting the result transformation step and directly outputting compliant dimensions, which greatly improves the efficiency of design iteration; at the same time, it sets the specification limits as direct constraints, avoiding complex manual judgment, and achieves precise alignment between the optimization process and engineering specifications, ensuring that the solution is compliant and reliable.

[0058] This embodiment replaces the limitations of traditional trial-and-error methods with systematic multi-parameter collaborative optimization. This method fully considers the coupling effects between various design variables to find the global optimal solution, and the results are highly reliable through final verification.

[0059] This embodiment replaces high-cost simulation analysis with a highly efficient proxy model, reducing optimization calculation time from weeks or even months to days, greatly improving the speed of design iteration and significantly shortening the product development cycle.

[0060] This embodiment uses security constraints as rigid boundaries for optimization and sets up a dual verification mechanism of "surrogate model optimization - original model verification", which successfully resolves the contradiction between security and economy and provides an advanced technical approach that is safe, reliable and maximizes economic benefits.

[0061] Example 2: Based on Example 1, this example provides a lightweight design method for marine structural pipe nodes based on response surface methodology. Taking a typical multi-branch complex spatial pipe node in the superstructure of a large marine converter station as the optimization object, the application process of the method in Example 1 is described in detail.

[0062] like Figure 2 As shown, the pipe node 2131 includes a first connecting pipe 3102, a second connecting pipe 3103, a third connecting pipe 3036, a fourth connecting pipe 3045, and a fifth connecting pipe 3054.

[0063] To more clearly define the application scenarios of this invention, the types of nodes involved in the platform are first categorized. Based on the form and function of the connecting members, platform nodes are mainly divided into four categories: first, steel-to-steel nodes bearing deck loads; second, steel-to-pipe nodes connecting deck beams and columns; third, complex spatial pipe nodes forming the core of the main frame and connecting the main columns and multiple large-diameter diagonal braces; and fourth, special nodes such as LMUs connecting the jacket structure. The pipe node 2131 selected in this embodiment belongs to the third category, "complex spatial pipe nodes." These nodes are located at the structural stress hubs, have the most complex geometric topology, and are a key focus of lightweight design.

[0064] The initial design parameters of the pipe joint are: main pipe (P1200×60), diagonal brace 1 (P1200×40), diagonal brace 2 (P1200×40), diagonal brace 3 (P1200×50), diagonal brace 4 (P600×30), with an initial total structural weight of 56.08 tons and a maximum stress ratio of 0.561 under extreme working conditions.

[0065] Preliminary analysis indicates that the fatigue damage at this node is minimal, and its strength far exceeds design requirements. Furthermore, the ultimate strength exhibits a large safety margin (UC value of 0.561), suggesting that strength is the primary design concern for this node, and that there is significant potential for optimization and weight reduction.

[0066] First, a parametric 3D solid model of the target pipe node is established using general-purpose finite element analysis software. The objective function of this model is defined as minimizing the total weight of the node's related components, which can be expressed by the following formula: ; in, This represents the total weight of the node. It is the outer diameter of the main tube, because it constitutes the main body of the structure, therefore... Treat it as a constant. These are key design variables defined in subsequent steps.

[0067] To ensure the absolute safety of the optimized structure, this step sets strict multiple constraints: First, there is the ultimate strength constraint, which requires that under all preset extreme load combinations, the strength check stress ratio at each connection weld of the node must meet the following requirements. as well as The requirements, among which, The strength-pressure ratio, As a load-stress ratio, this limit of 0.8 provides a 20% safety margin compared to the standard requirement of 1.0.

[0068] Secondly, there are manufacturing process constraints, requiring that the outer diameter of the component represented by all design variables must meet certain requirements. Minimum requirements.

[0069] Finally, there are geometric validity constraints. To ensure the physical meaning of the model, it is also necessary to satisfy geometric constraints defined by software or specifications, such as the outer diameter of the main pipe being greater than the outer diameter of a specific branch pipe.

[0070] The geometric parameters most sensitive to the total weight and mechanical properties of the nodes were identified. Based on the analysis of the force transmission path of the nodes, the following parameters were determined. The three key dimensions are used as design variables, namely: : Outer diameter of the main pipe (mm). Outer diameter (mm) of diagonal brace 1 and diagonal brace 2. : Diagonal brace 3 outer diameter (mm). Diagonal brace 4 outer diameter (mm).

[0071] To ensure the effectiveness of the optimization process, this step is based on initial design and engineering experience, whereby... The remaining design variables have reasonable optimization boundaries set: ; This range ensures that while covering a broad design space from the initial design to the constraint boundaries, unrealistic combinations of dimensions are avoided.

[0072] The Latin hypercube sampling method is used to generate experimental sample points within the four-dimensional design space defined in step S2. This method ensures that the sampling points have excellent uniformity and representativeness within the range of values ​​for each variable. In this embodiment, a total of 16 representative parameter combination sample points were generated.

[0073] These 16 sets of parameters were sequentially substituted into the established finite element model to perform a complete structural static analysis. For each sample point, the precise total structural weight and the eight key stress ratios generated by the four diagonal braces under preset extreme conditions were calculated and recorded. This resulted in a complete database containing 16 rows of data, with design variables as input and structural response as output.

[0074] Establish an explicit mathematical model that can replace time-consuming finite element method (FEM) calculations. This process requires building an independent response surface model for each structural response. Ultimately, this will generate a model targeting the optimization objective. The general mathematical form of these response surface models can be expressed as: ; in, These are predicted response values, such as weight or stress ratio. It is a design variable. These are the undetermined coefficients obtained through regression analysis.

[0075] In this embodiment, nine response surface proxy models were constructed, including the total weight and eight key stress ratios. The specific function expressions of some of the key models are listed below: Total weight response surface model: ; diagonal brace 1 The response surface model is as follows: Figure 3 , Figure 4 and Figure 5 As shown, the fitting residual analysis plot is displayed: ; ; To ensure the accuracy of the surrogate model, the accuracy of all established response surface models was verified. The results show that the coefficient of determination R² of all models is greater than 0.998, and the relative root mean square error RRMSE is much less than 0.05. In addition, the residual analysis plot also shows that the error is randomly distributed without any trend. This proves that the constructed surrogate model has extremely high fitting accuracy and can completely replace the original finite element model for subsequent optimization calculations.

[0076] Based on the aforementioned precise surrogate model, the optimal design scheme is quickly solved. The established series of response surface functions are then compared with the defined objective function. Combined with constraints, this constitutes a complete, explicit optimization problem.

[0077] Mature optimization algorithms, such as multi-objective optimization algorithms based on Pareto front analysis or sequential quadratic programming, are used to solve the aforementioned explicit mathematical problems. The solver can explore the entire design space within seconds or minutes and find solutions that satisfy all constraints. The minimum solution. After algorithmic solving and engineering rounding, the optimal combination of design variables is obtained as follows: , , , .

[0078] The final results of this invention were rigorously verified by inputting the aforementioned optimal size parameters into the original numerical model and performing an independent and complete verification calculation, resulting in the verification results shown in Table 1: Table 1 Result Verification Table

[0079] As shown in Table 1, the verification results are in high agreement with the predicted values ​​of the response surface model. For example, the predicted load-stress ratio of brace 3 is 0.4754, while the actual calculated value is 0.477. The final verification results show that the optimized maximum stress ratio of the node is 0.798, strictly meeting the design constraint of less than 0.8. The total structural weight was significantly reduced from the initial 56.08 tons to 14.23 tons, achieving extreme lightweighting while ensuring safety, with a weight reduction effect of up to 74%, fully demonstrating the advanced nature and enormous engineering and economic value of this invention.

[0080] Example 3: This embodiment provides a lightweight design system for marine structural pipe nodes based on the response surface methodology, including: The objective function creation module is configured to: create a parameterized 3D solid model of the target pipe node; and create an objective function with the goal of minimizing the total weight of the structural pipe node and the constraint that the ultimate strength stress ratio is not greater than a preset allowable value. The sample point generation module is configured to generate a series of test sample points based on the 3D solid model and the objective function using Latin hypercube sampling. The response value extraction module is configured to extract the structural response value corresponding to each sample point. The polynomial function creation module is configured to: obtain a polynomial function by fitting the response surface method based on the structural response value; The design module is configured to: obtain a lightweight design scheme based on a polynomial function.

[0081] The working method of the system is the same as that of the response surface methodology-based lightweight design method for marine structural pipe nodes in Embodiment 1 or Embodiment 2, and will not be repeated here.

[0082] Example 4: This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the lightweight design method for marine structural pipe nodes based on the response surface methodology described in Embodiment 1.

[0083] Example 5: This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. When the processor executes the program, it implements the steps of the lightweight design method for marine structural pipe nodes based on the response surface methodology described in Embodiment 1.

[0084] Example 6: This embodiment provides a computer program product, which includes a computer program. When the computer program is executed by a processor, it implements the steps of the lightweight design method for marine structural pipe nodes based on the response surface methodology described in Embodiment 1.

[0085] The above description is merely a preferred embodiment of this practice and is not intended to limit the scope of this practice. Various modifications and variations can be made to this practice by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this practice should be included within the protection scope of this practice.

Claims

1. A lightweight design method for pipe nodes in marine structures based on response surface methodology, characterized in that, include: Establish a parameterized 3D solid model of the target pipe node; with the goal of minimizing the total weight of the structural pipe node and the constraint that the ultimate strength stress ratio is not greater than the preset allowable value, establish an objective function; Based on the three-dimensional solid model and the objective function, a series of experimental sample points are generated using Latin hypercube sampling. Extract the structural response value corresponding to each sample point; Based on the structural response values, a polynomial function is obtained by fitting using the response surface methodology. Based on the polynomial function, a lightweight design scheme is obtained.

2. The lightweight design method for marine structural pipe nodes based on response surface methodology as described in claim 1, characterized in that, When determining the constraints, the strength check stress ratio at all connection welds must meet the allowable stress ratio limit; the constraints also include geometric dimensions.

3. The lightweight design method for marine structural pipe nodes based on response surface methodology as described in claim 1, characterized in that, When generating samples using Latin hypercube sampling, the constraint is that the wall thickness of the main pipe is greater than that of the branch pipe, ensuring that the combination of sample points conforms to mechanical constraints.

4. The lightweight design method for marine structural pipe nodes based on response surface methodology as described in claim 1, characterized in that, For each sample point combination, structural analysis is performed using numerical simulation. First, an overall platform model is established to extract the axial force, shear force, and bending moment of the adjacent sections of the target node. Then, a solid sub-model is established. Based on the rule that the node load is along the global coordinate and the member load is along the local coordinate, the internal force data is applied as boundary loads and analyzed to finally obtain the accurate stress ratio.

5. The lightweight design method for marine structural pipe nodes based on response surface methodology as described in claim 1, characterized in that, The fitted polynomial function is: ； in, It is the structural response value predicted by the model; and These are design variables; These are the undetermined coefficients obtained through regression analysis.

6. The lightweight design method for marine structural pipe nodes based on response surface methodology as described in claim 1, characterized in that, Based on the polynomial function, objective function, and constraints, a sequential quadratic programming algorithm is used to solve the problem, resulting in a combination of design variables that minimizes the total weight of the structure while satisfying all stress ratios and other constraints.

7. A lightweight design system for marine structural pipe joints based on response surface methodology, characterized in that, include: The objective function creation module is configured to: create a parameterized 3D solid model of the target pipe node; and create an objective function with the goal of minimizing the total weight of the structural pipe node and the constraint that the ultimate strength stress ratio is not greater than a preset allowable value. The sample point generation module is configured to generate a series of test sample points based on the 3D solid model and the objective function using Latin hypercube sampling. The response value extraction module is configured to extract the structural response value corresponding to each sample point. The polynomial function creation module is configured to: obtain a polynomial function by fitting the response surface method based on the structural response value; The design module is configured to: obtain a lightweight design scheme based on a polynomial function.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the lightweight design method for marine structural pipe nodes based on the response surface methodology as described in any one of claims 1-6.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, When the processor executes the program, it implements the steps of the lightweight design method for marine structural pipe nodes based on the response surface methodology as described in any one of claims 1-6.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the steps of the lightweight design method for marine structural pipe nodes based on the response surface methodology as described in any one of claims 1-6.

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