Welding process parameter optimization method based on finite element simulation and response surface method

Abstract

The application discloses a welding process parameter optimization method based on finite element simulation and a response surface method, and is used for welding residual stress and deformation control problems of large and complex structures in a nuclear fusion device. The method is characterized in that: a thermal-mechanical coupling finite element model of a welding process is constructed, mechanical responses under different process parameter combinations are obtained, an approximate function relationship between process parameters and welding responses is established by using the response surface method, multi-objective optimization is realized at a mathematical model level, and an optimal process parameter combination meeting welding performance requirements is obtained. The application establishes a mathematical mapping model between process parameters and key performance indexes such as welding residual stress and deformation by using the response surface method, and then performs multi-objective optimization on the response surface, so that a large amount of repeated simulation and artificial judgment in a traditional trial-and-error method are avoided, and the optimization efficiency and systematization are significantly improved.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation and process optimization technology in welding manufacturing, specifically to a method for optimizing welding process parameters based on finite element simulation and response surface methodology. Background Technology

[0002] The development and construction of large-scale nuclear fusion devices involve numerous complex and precision-required welded components, such as vacuum chambers, cooling pipes, magnet support systems, and their connecting structures. These components are typically large in size, have complex welding paths, and uneven heat input, making them highly susceptible to significant residual stress and structural deformation during the welding process. This can severely impact the structural integrity, assembly accuracy, and operational reliability of the device.

[0003] To ensure welding quality, finite element simulation technology is widely used in engineering to model the welding thermo-mechanical process, predict the temperature field, stress field, and post-weld deformation, and assist in optimizing the welding sequence and process parameters. However, traditional simulation methods are mostly qualitative analyses or parameter trial and error, with limited exploration of the optimization space under the coupling of multiple parameters, making it difficult to achieve efficient optimization while ensuring accuracy.

[0004] In recent years, the integrated application of numerical optimization algorithms and simulation models has gradually emerged, especially the approximate modeling and multi-objective optimization methods represented by the response surface methodology (RSM), which have the advantages of high modeling efficiency and clear optimization strategies, and have already shown initial success in some welding process designs. However, there is still a lack of a general method applicable to the welding conditions of complex structures in nuclear fusion devices, which can systematically integrate finite element simulation and parameter optimization to achieve effective prediction and active control of welding residual stress and deformation.

[0005] Therefore, there is an urgent need to establish a unified framework that integrates welding finite element simulation and multi-objective optimization methods to improve the efficiency of welding process design and the ability to predict structural service performance.

[0006] I will also introduce the relevant shortcomings of existing technologies:

[0007] Currently, the following technical solutions are commonly used in engineering to control welding residual stress and welding deformation:

[0008] (1) Process optimization method based on empirical rules

[0009] In engineering practice, there is a heavy reliance on the experience of welding process personnel to optimize processes by controlling heat input, welding sequence, cooling methods, and fixture arrangement. While these methods are simple to implement, the optimization results depend on experience-based judgment, lack systematicity and repeatability, and are difficult to handle the coupled optimization needs of multiple parameters and objectives under complex structures.

[0010] (2) Welding process simulation method based on finite element simulation

[0011] Utilizing finite element platforms such as Abaqus, SYSWELD, and WeldSim for welding thermo-mechanical coupling simulation has become an important method for predicting residual stress and deformation. By simulating the effects of heat source loading, changes in material thermo-mechanical properties, and welding sequence, quantitative prediction of the welding process can be achieved. However, this type of method is mainly used for result evaluation, lacks effective coupling with optimization algorithms, and does not have automatic optimization capabilities. It requires a large amount of manual trial calculation to complete parameter adjustments, resulting in low efficiency.

[0012] (3) Optimization method for process parameters based on optimization algorithm

[0013] Some studies have introduced optimization strategies such as genetic algorithms, particle swarm optimization, or response surface methodology to optimize welding parameters. However, in practical applications, the optimization module and physical simulation are often disconnected, resulting in problems such as low data interaction efficiency, insufficient simulation accuracy, or slow convergence speed. This is especially true in large-scale structures such as nuclear fusion devices, where there is a lack of an integrated optimization framework that can adapt to complex boundary conditions, nonlinear material behavior, and the need for high-precision prediction.

[0014] In summary, existing technologies generally have the following shortcomings when welding complex structural components of nuclear fusion devices:

[0015] ① The lack of scientific modeling and systematic analysis methods in process optimization makes it difficult to meet the requirements of high-precision welding;

[0016] ② Finite element simulation and optimization algorithms have not been effectively integrated, and there is a lack of automated parameter optimization capabilities;

[0017] ③ Insufficient ability to coordinate and control multiple objectives (such as residual stress and deformation), and limited optimization strategies;

[0018] ④ Practical and engineering tools for high-reliability fields such as nuclear fusion are not yet mature. Summary of the Invention

[0019] The present invention proposes a method, equipment, and storage medium for optimizing welding process parameters based on finite element simulation and response surface methodology, which can at least solve one of the technical problems in the background art.

[0020] To achieve the above objectives, the present invention adopts the following technical solution:

[0021] A welding process parameter optimization method based on finite element simulation and response surface methodology involves the following steps performed using computer equipment:

[0022] S1. First, based on the characteristics of the welding process, select process parameters that are closely related to heat input and structural stiffness as design variables; and set the optimization objective function to clarify the input and output indicators of the optimization task.

[0023] Step 2: Based on the design variables and objective function determined by S1, representative parameter sample points are generated using the central composite design in the response surface methodology; each sample point is a set of process parameter combinations, which serve as input for subsequent finite element simulations.

[0024] Step 3: Establish a three-dimensional thermo-mechanical coupling model using the finite element platform, and simulate the heat input using a double ellipsoidal heat source model; input the parameter combination generated in step 2 into the three-dimensional thermo-mechanical coupling model established on the finite element platform to form the corresponding simulation conditions. The output of the model is the temperature field, stress field and deformation results.

[0025] Step 4: Run the finite element model sequentially on all sample points generated in Step 2, and use Python scripts to perform batch calculations and automated data extraction; this step outputs residual stress values, deformation amounts, and thermal cycling characteristic data under various process parameter combinations, forming a complete dataset;

[0026] Step 5: Import the input and output data obtained in Step 4 into the response surface modeling module, and establish quadratic polynomial approximation functions for residual stress and post-weld deformation respectively; the response surface function serves as an approximate expression of the simulation results, realizing the mathematical mapping between process parameters and performance indicators;

[0027] Step 6: Perform optimization on the response surface function constructed in Step 5. Use the weighted sum method or goal programming optimization strategy to comprehensively evaluate multiple objectives and search for one or more optimal solutions that meet the performance balance requirements, forming a Pareto solution set. The output of this step is the candidate optimal combination of process parameters.

[0028] Step 7: Re-input the candidate optimal solution obtained in Step 6 into the finite element model for verification calculation; compare the error between the simulation results and the response surface prediction values. If the error is within the preset tolerance range, the optimal solution is confirmed; if the error exceeds the limit, return to Step 2, add sample points and update the response surface model to form a closed loop iteration.

[0029] Step 8: Finally, output the verified optimal combination of process parameters and apply it to the actual welding process card preparation, fixture design, and welding sequence planning stages, directly providing guidance for engineering practice.

[0030] In another aspect, the present invention also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method described above.

[0031] In another aspect, the present invention also discloses a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method described above.

[0032] As can be seen from the above technical solutions, the present invention aims to solve the problems of residual stress and welding deformation control in the welding process of key structures of large nuclear fusion devices, especially the following key technical problems:

[0033] ① Coupled modeling problem of the influence of multiple process factors on welding mechanical response

[0034] Welded components in nuclear fusion devices are characterized by large size, complex geometry, and diverse boundary constraints. During the welding process, multiple factors, such as heat input, speed, path, cooling method, and fixture constraints, jointly influence post-weld stress and deformation. This invention aims to establish a high-fidelity finite element modeling method that can effectively simulate the combined effects of multiple process parameters and supports thermo-mechanical coupling analysis.

[0035] ② The integration efficiency problem between high-cost simulation solutions and parameter optimization

[0036] The separation of traditional simulation and optimization processes leads to low efficiency and high computational cost in parameter calculation, making it unsuitable for efficient optimization under complex structures. This invention aims to construct a framework that deeply integrates finite element simulation and optimization algorithms, enabling automatic parameter retrieval, batch result extraction, and iterative optimization control, thereby improving optimization efficiency.

[0037] ③ Optimization modeling problem of coordinated control of multi-objective performance (stress and deformation)

[0038] In practical engineering, minimizing residual stress and minimizing post-weld deformation often conflict. This invention introduces approximate modeling techniques such as response surface methodology to construct a mapping relationship between process parameters and multiple objectives, and combines this with appropriate multi-objective optimization algorithms to achieve coordinated control of welding performance indicators and optimal solution search.

[0039] ④ Coupling and automation issues between simulation platform and script control program

[0040] Since the Abaqus finite element simulation platform often uses Fortran user subroutines to control physical behaviors such as heat source loading, and parameter optimization is mostly based on Python for scheduling and algorithm implementation, this invention needs to build a joint driver architecture of Abaqus + Fortran + Python to realize an integrated automated process of welding simulation modeling, heat source control, automatic parameter modification, batch calculation and data transfer.

[0041] This invention relates to a welding process parameter optimization method based on finite element simulation and response surface methodology. Specifically, it involves a method that combines finite element welding simulation with response surface methodology to systematically optimize welding process parameters through multi-objective optimization. This method is applicable to the prediction and control of residual stress and welding deformation during the welding process and can be widely applied to the optimization of welding process design and manufacturing processes for key components of nuclear fusion devices.

[0042] This invention provides a welding process parameter optimization method based on finite element simulation and response surface methodology. Compared with existing techniques that rely on experience-based adjustment of welding process parameters or that separate finite element simulation and optimization, this method has the following significant advantages:

[0043] (1) To achieve systematic and multi-objective optimization design of welding process parameters.

[0044] This invention establishes a mathematical mapping model between process parameters and key performance indicators such as welding residual stress and deformation using the response surface methodology. Then, it performs multi-objective optimization on the response surface, avoiding a large amount of repetitive simulation and manual judgment in the traditional trial-and-error method, and significantly improving optimization efficiency and systematicity.

[0045] (2) Integrate finite element simulation and parameter optimization processes to build a unified closed-loop platform.

[0046] This invention employs deep integration of Python scripts with Abaqus and Fortran subroutines, streamlining the entire process of parameter setting, model solving, result extraction, fitting modeling, and optimization decision-making. This enables integrated automatic operation of welding simulation and optimization, significantly reducing the burden of manual operation.

[0047] (3) The double ellipsoidal heat source model and thermo-mechanical coupling theory are adopted to enhance the physical realism.

[0048] The welding heat input model is based on the Goldak double ellipsoid model, which can accurately characterize the asymmetric weld depth and heat conduction characteristics in the complex structure of nuclear fusion devices; combined with transient heat conduction and elastoplastic mechanics models, it ensures the accuracy of prediction of residual stress and post-weld deformation.

[0049] (4) The optimization algorithm is simple and stable, and is suitable for engineering deployment of large-scale nuclear fusion structures.

[0050] This invention directly performs multi-objective optimization based on response surface functions, and uses weighted summation or goal programming to replace evolutionary methods such as genetic algorithms and particle swarm optimization. This avoids the dramatic increase in simulation computation caused by global search, and the optimization process is more stable and easier to converge. It is more suitable for solving welding scenarios with complex welds and numerous operating conditions in nuclear fusion devices.

[0051] (5) It is easy to promote and apply, and can adapt to complex working conditions and customized target needs.

[0052] The proposed method can be used not only for optimizing basic parameters such as welding heat input and speed, but also for higher-level process design problems such as fixture layout, cooling method, and welding sequence. It has good scalability and adaptability and is suitable for large-scale engineering application and promotion.

[0053] (6) Improve the service performance of welded structures and enhance the overall operational reliability of the equipment.

[0054] By optimizing parameter combinations, the peak value of residual stress and the total structural deformation can be effectively reduced, which helps to improve the positioning accuracy and welding joint quality of key components and auxiliary equipment of nuclear fusion devices, thereby improving the system's operational stability and structural safety redundancy from the source.

[0055] (7) Support the integration of iterative engineering design and digital manufacturing processes

[0056] The optimization results can be directly output for welding process card compilation, automated welding equipment control, or virtual assembly analysis, supporting the digital and intelligent transformation of welding processes and providing effective support for the full life cycle simulation design of nuclear fusion devices. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the optimization method provided in an embodiment of the present invention;

[0058] Figure 2 This is a schematic diagram of the weld pool distribution provided in an embodiment of the present invention;

[0059] Figure 3 A schematic diagram of welding residual stress distribution provided in an embodiment of the present invention;

[0060] Figure 4 This is a schematic diagram of welding deformation distribution provided for an embodiment of the present invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0062] This invention proposes a welding process parameter optimization method based on finite element simulation and response surface methodology, addressing the problem of residual stress and deformation control in the welding of large and complex structures in nuclear fusion devices. This method constructs a thermo-mechanical coupled finite element model of the welding process to obtain the mechanical response under different combinations of process parameters. Then, it uses response surface methodology to establish an approximate functional relationship between the process parameters and the welding response, thereby achieving multi-objective optimization at the mathematical model level and obtaining the optimal combination of process parameters that meets the welding performance requirements.

[0063] This invention proposes a welding process parameter optimization method based on finite element simulation and response surface methodology. The overall process includes parameter definition, experimental design, finite element modeling, batch simulation, response surface construction, multi-objective optimization, simulation verification, and final process output. Figure 1 It visually demonstrates the sequence of each step and the input-output relationship, reflecting the closed-loop optimization logic of the method.

[0064] Specifically, the following steps are included:

[0065] Step 1: Determine the optimization parameters and objective function

[0066] First, based on the characteristics of the welding process, process parameters closely related to heat input and structural stiffness (such as arc current, welding voltage, welding speed, heat source front-to-back ratio, heat source expansion parameters, fixture stiffness, etc.) are selected as design variables; and optimization objective functions (such as maximum residual stress and maximum post-weld deformation) are set to clarify the input and output indicators of the optimization task.

[0067] Step 2: Experimental Design and Parameter Sample Generation

[0068] Based on the design variables and objective function determined by S1, representative parameter sample points are generated using the central composite design (CCD) method in the response surface methodology. Each sample point represents a set of process parameter combinations, which serve as input for subsequent finite element simulations.

[0069] Step 3: Establish a thermo-mechanical coupled finite element model

[0070] A three-dimensional thermo-mechanical coupling model is established using a finite element platform (such as Abaqus), and the thermal input is simulated using a double ellipsoidal heat source model. The parameter combination generated in step 2 is input into this model to form the corresponding simulation conditions. The model outputs the temperature field, stress field, and deformation results.

[0071] Step 4: Batch Simulation and Data Extraction

[0072] The finite element model is run sequentially on all sample points generated in step 2, and batch calculations and automated data extraction are achieved using Python scripts. This step outputs residual stress values, deformation amounts, and thermal cycling characteristic data under various combinations of process parameters, forming a complete dataset.

[0073] Step 5: Construct the response surface function

[0074] The input-output data obtained in step 4 is imported into the response surface modeling module, and quadratic polynomial approximation functions are established for residual stress and post-weld deformation, respectively. The response surface function serves as an approximate expression of the simulation results, realizing the mathematical mapping between process parameters and performance indicators.

[0075] Step 6: Perform multi-objective optimization based on response surface methodology

[0076] Optimization is performed on the response surface function constructed in step 5. Multiple objectives (such as stress and deformation) are comprehensively evaluated using optimization strategies such as weighted summation or goal programming to search for one or more optimal solutions that satisfy performance balance requirements, forming a Pareto solution set. The output of this step is the candidate optimal combination of process parameters.

[0077] Step 7: Simulation Verification and Error Assessment

[0078] The candidate optimal solution obtained in step 6 is re-inputted into the finite element model for verification calculation. The error between the simulation results and the response surface prediction values ​​is compared. If the error is within the preset tolerance range, the optimal solution is confirmed; if the error exceeds the tolerance range, return to step 2, add sample points and update the response surface model to form a closed-loop iteration.

[0079] Step 8: Output optimal parameters to guide welding design.

[0080] The final output is the optimal combination of process parameters that has been verified, and it is applied to the actual welding process card preparation, fixture design, welding sequence planning and other aspects, directly providing guidance for engineering practice.

[0081] The logical relationship between the above 8 steps is as follows:

[0082] ①S1 and Step 2: Define the problem and generate input;

[0083] ② Steps 3 and 4: Transform the input into output data through simulation;

[0084] ③ Steps 5 and 6: Based on the database of simulation output results, establish the input-output mapping function and perform optimization;

[0085] ④ Step 7: Verify and form a feedback loop;

[0086] ⑤ Step 8: Output the final optimization results and apply them to actual projects.

[0087] The following provides further details:

[0088] S1: Determine the optimization parameters and objective function

[0089] (1) The design variables (process parameters) closely related to welding heat input and structural stiffness are determined as follows:

[0090] ① Arc current Unit A;

[0091] ② Welding voltage Unit: V;

[0092] ③ Welding speed Unit: mm / s;

[0093] ④ Comparison of heat source before and after Dimensionless;

[0094] ⑤ Heat source expansion parameters The unit is mm;

[0095] ⑥ Fixture stiffness , unit N / mm.

[0096] (2) Set two optimization objective functions:

[0097] ① Maximum residual welding stress: Unit: MPa;

[0098] ② Maximum deformation after welding: , unit mm.

[0099] parameter This refers to the combination of welding process parameters, which is a set of input conditions that affect welding residual stress and deformation results; It is not a single variable, but a "parameter vector" composed of multiple process parameters, including:

[0100] Arc current I, in amperes (A);

[0101] Welding voltage U, in V;

[0102] Welding speed v, in mm / s;

[0103] The ratio f before and after the heat source is dimensionless.

[0104] Heat source expansion parameters a, b, c, in mm;

[0105] Fixture stiffness K f , unit N / mm.

[0106] Step 2: Experimental Design and Parameter Sample Generation

[0107] Experimental schemes were constructed using the Central Composite Design (CCD) approach from the response surface methodology. Generate under each parameter dimension 1 sample point.

[0108] Each sample point represents a set of parameter combinations. This corresponds to one simulation condition.

[0109] The Python script automatically creates *.inp input files and sets the heat source parameters (using Fortran) to achieve batch processing of simulations.

[0110] n represents the number of design variables (parameters), that is, the number of process parameters involved in the optimization. For example, in this invention, 6 parameters are considered (current, voltage, welding speed, heat source front-to-back ratio, heat source broadening, and fixture stiffness), then n=6.

[0111] N represents the total number of test sample points, i.e., the number of simulated operating conditions required. The calculations based on the central composite design and construction test scheme yielded the following: ;

[0112] This represents the orthogonal combination point (cube vertex) of all parameters.

[0113] This represents the star points in the positive and negative directions of each parameter axis (used to capture curve effects).

[0114] c represents the number of center points, used to evaluate simulation repeatability and model error; typically, 3 to 6 are used.

[0115] i represents the sample point number, i.e., the i-th parameter combination, which corresponds to a specific combination of welding conditions.

[0116] Step 3: Establish a thermo-mechanical coupled finite element model

[0117] A three-dimensional thermo-mechanical coupling model was built in Abaqus, using a double ellipsoidal heat source model (Goldak model) as the thermal input:

[0118]

[0119] In the formula,

[0120] This is the transient volumetric heat flux density, in W / m³. 3 ;

[0121] The heat input power is expressed in watts (W), and the calculation formula is as follows:

[0122]

[0123] Thermal efficiency, which depends on the welding method and is dimensionless;

[0124] Welding voltage, unit: V;

[0125] Welding current, in amperes (A).

[0126] The semi-major axis of the heat source in the triaxial direction, in mm;

[0127] The ratio of the front / back heat source is... / , dimensionless, and satisfying the following relationship:

[0128]

[0129] The heat conduction equation is:

[0130]

[0131] In the formula,

[0132] The density of the material is expressed in kg / m³.

[0133] This is the specific heat capacity at constant pressure of the material, expressed in J / (kg*K).

[0134] The thermal conductivity of the material is expressed in W / (m*K).

[0135] Temperature, in Kelvin (K).

[0136] This is the heat source term, with units of W / m^3.

[0137] After obtaining the temperature field, calculations of thermally induced deformation and stress evolution are performed. A thermo-elastic-plastic constitutive model is used, and its formulas are as follows:

[0138]

[0139] In the formula,

[0140] This is the stress tensor, with units of Pa.

[0141] This is the elastic stiffness tensor, with units of Pa.

[0142] The total strain tensor is dimensionless;

[0143] The coefficient of thermal expansion is 1 / K.

[0144] The initial temperature is expressed in Kelvin (K).

[0145] like Figure 2As shown, this invention employs the Goldak double ellipsoidal heat source model in finite element simulation, which can realistically reproduce the shape and distribution of the weld pool. By setting parameters such as arc current, voltage, and welding speed, the characteristics of weld depth and width under different process conditions can be reflected, thus providing an accurate thermal input basis for subsequent stress and deformation analysis.

[0146] Step 4: Batch Simulation and Data Extraction

[0147] After running the Abaqus analysis for each parameter combination, the following results were automatically extracted using a Python script (calling the abaqusodbAccess module):

[0148] Maximum residual stress: ;

[0149] Maximum displacement deformation: ;

[0150] Peak temperature of thermal cycling and cooling rate.

[0151] All results are output in CSV format, and data pairs are constructed. .

[0152] : Represents the i-th combination of welding process parameters, which is the input condition for a simulation condition, including several specific parameters:

[0153] Arc current (unit: A)

[0154] Welding voltage (unit: V)

[0155] Welding speed (unit: mm / s)

[0156] The ratio before and after the heat source (dimensionless)

[0157] Heat source expansion parameters (unit: mm)

[0158] Fixture stiffness (unit: N / mm)

[0159] This represents the maximum value of welding residual stress calculated under the i-th parameter combination, i.e., the stress peak value in the simulation result, in MPa.

[0160] This represents the maximum deformation after welding calculated under the i-th parameter combination, i.e., the maximum displacement of the structure after welding, in mm.

[0161] like Figure 3As shown, the residual stress distribution during the welding process was obtained through finite element analysis. The stress concentration in the weld and adjacent areas can be observed in the figure, especially the peak stress regions in the transverse and longitudinal directions. This result verifies the quantitative prediction capability of the proposed method for the welding stress field and provides a reference for optimizing process parameters to reduce peak residual stress.

[0162] like Figure 4 As shown, the finite element method (FEM) yielded the structural deformation distribution after welding. The figure reflects the warping and displacement characteristics of the welded area and the overall component, visually demonstrating the spatial distribution of post-weld deformation. Combined with response surface optimization results, the overall deformation amplitude can be effectively reduced, improving the assembly accuracy of the welded structure.

[0163] Step 5: Construct the response surface function

[0164] Two objective functions are constructed using a quadratic multinomial regression model (Quadratic RSM):

[0165]

[0166] in,

[0167] For predicting residual stress, the unit is MPa;

[0168] To predict the maximum deformation, the unit is mm;

[0169] Standardized values ​​for the parameters;

[0170] For the regression coefficients, the least squares method is used for fitting.

[0171] The fitting effect is determined by the coefficient of determination. And root mean square error (RMSE) assessment, typically requires ;

[0172] Where k represents the objective function number.

[0173] This invention has two optimization objectives:

[0174] When k=1, f1(x) represents the maximum value of welding residual stress (unit MPa).

[0175] When k=2, f2(x) represents the maximum deformation after welding (in mm).

[0176] i and j: both represent the ordinal numbers (parameter numbers) of the design variables, and i ≠ j.

[0177] This is used to identify each welding process parameter:

[0178] When i / j=1, x1 is the arc current (A);

[0179] When i / j=2, x2 is the welding voltage (V);

[0180] When i / j=3, x3 is the welding speed (mm / s);

[0181] When i / j=4, x4 is the ratio of the heat source before and after (dimensionless).

[0182] When i / j=5, x5 is the heat source widening parameter (mm);

[0183] When i / j=6, x6 is the stiffness of the fixture (N / mm).

[0184] item This indicates the linear effect of each parameter on the result;

[0185] item This indicates the second-order nonlinear effect of the parameter;

[0186] item This represents the interaction effect between parameters i and j (i.e., the combined effect of changes in two different parameter combinations on the result).

[0187] Step 6: Perform multi-objective optimization based on response surface methodology

[0188] The following two in-response surface optimization strategies are adopted:

[0189] Method A: Weighted Sum Method

[0190] Construct the comprehensive objective function:

[0191]

[0192]

[0193] For different weight combinations Optimize the solution and search for the minimum value. This forms the Pareto front.

[0194] : Represents the combination of welding process parameters, i.e., the set of optimized input variables, including:

[0195] Arc current (A)

[0196] Welding voltage (V)

[0197] Welding speed (mm / s)

[0198] The ratio before and after the heat source (dimensionless)

[0199] Heat source expansion parameters (mm)

[0200] Fixture stiffness (N / mm)

[0201] f1(x): represents the maximum value of welding residual stress, which is the first optimization objective function; the unit is MPa.

[0202] f2(x): represents the maximum deformation after welding, which is the second optimization objective function; the unit is mm.

[0203] w1 and w2 represent the weight coefficients of the two objective functions, used to reflect the importance of each objective.

[0204] w1 corresponds to the weight of f1(x) (stress index);

[0205] w2 corresponds to the weight of f2(x) (the deformation index);

[0206] Both are dimensionless values ​​(unitless) and satisfy w1+w2=1.

[0207] Method B: Goal Programming

[0208] Given the maximum allowable stress and deformation:

[0209]

[0210]

[0211] Using the sum of squared errors as the objective:

[0212]

[0213] Find the optimal parameter combination .

[0214] : Represents the combination of welding process parameters, i.e., the set of optimized input variables, including:

[0215] Arc current (A)

[0216] Welding voltage (V)

[0217] Welding speed (mm / s)

[0218] The ratio before and after the heat source (dimensionless)

[0219] Heat source expansion parameters (mm)

[0220] Fixture stiffness (N / mm)

[0221] f1(x): represents the maximum value of welding residual stress, which is the first optimization objective function; the unit is MPa.

[0222] f2(x): represents the maximum deformation after welding, which is the second optimization objective function; the unit is mm.

[0223] : Indicates the maximum allowable residual stress limit, i.e., the upper limit allowed in engineering design or material specifications, in MPa.

[0224] : Indicates the maximum allowable deformation limit, that is, the upper limit allowed in the structural assembly or tolerance requirements, in mm.

[0225] : Indicates the desired target residual stress value (usually less than or close to) ), unit: MPa.

[0226] : Indicates the desired target deformation value (usually less than or close to) ), unit: mm.

[0227] Step 7: Simulation Verification and Error Assessment

[0228] The optimal solution Input the Abaqus model and re-simulate to extract the actual data. Error analysis was performed between the predicted and actual values:

[0229]

[0230] If error If the optimization is successful, then return to step 2 for local augmentation sampling.

[0231] k: Represents the objective function number.

[0232] This invention has two optimization objectives:

[0233] When k=1, f1(x) represents the maximum value of welding residual stress (unit MPa).

[0234] When k=2, f2(x) represents the maximum deformation after welding (in mm).

[0235] f1(x): represents the maximum value of welding residual stress, which is the first optimization objective function; the unit is MPa.

[0236] f2(x): represents the maximum deformation after welding, which is the second optimization objective function; the unit is mm.

[0237] : Represents the maximum value of welding residual stress obtained through finite element simulation, in MPa.

[0238] : Represents the maximum deformation after welding obtained through finite element simulation, in mm.

[0239] : Represents the relative error percentage of the k-th objective function, that is, the deviation between the predicted value and the actual simulation value.

[0240] Step 8: Output optimal parameters to guide welding design.

[0241] Output the final optimal combination of process parameters. For guidance:

[0242] Welding process card preparation;

[0243] Fixture design and layout;

[0244] Path planning and devising of adaptation strategies.

[0245] In practical implementation, this invention can improve the accuracy of residual stress prediction and the reliability of local yield judgment under welding thermal cycling by introducing a temperature-dependent nonlinear constitutive model of materials, including the temperature coupling relationship between dynamic yield stress, elastic modulus, and coefficient of thermal expansion. The material model used can be based on J2 viscoplasticity theory or Chaboche nonlinear strengthening model.

[0246] This invention can improve the accuracy of predictions in the neighborhood of the optimal solution and enhance the global stability of the optimized solution by constructing a dynamically updated response surface model (AdaptiveRSM), performing local denser sampling in the region near the Pareto boundary after initial optimization, and retraining the local response surface function.

[0247] This invention can consider the influence of changes in the metal microstructure on material properties during thermal analysis by integrating the heat-affected zone (HAZ) and microstructure evolution model. It is particularly suitable for high-strength steel, stainless steel or dissimilar material welded structures, and further improves the physical consistency of stress and deformation prediction.

[0248] This invention can improve the adaptability of process parameters to service performance by expanding the types and number of optimization objective functions, such as simultaneously introducing performance indicators such as weld joint fatigue life, weld zone cooling rate, and fusion ratio.

[0249] This invention can be integrated with a welding robot control system to convert optimized parameter combinations and welding path control signals into PLC or NC control instructions, which can be used to directly drive automatic welding equipment and realize closed-loop control from simulation to actual welding.

[0250] This invention can optimize the welding sequence loading order by coupling a welding sequence planning module, while keeping the total heat input constant, so as to control the heat accumulation path and heat gradient direction, thereby further reducing the risk of total deformation and structural warping after welding.

[0251] To illustrate the practical feasibility of this invention, the following uses a common thick-plate T-joint welding structure found in nuclear fusion devices as an example to describe how to perform simulation modeling, response surface construction, and optimization design of welding process parameters based on the method of this invention. This T-joint structure consists of two metal plates of similar thickness (base material A and base material B), connected by multi-pass, multi-layer welding. This embodiment is carried out according to the following steps:

[0252] S1: Parameter Definition and Optimization Target Setting

[0253] Select the following design variables:

[0254] ① Arc current Unit A;

[0255] ② Welding voltage Unit: V;

[0256] ③ Welding speed Unit: mm / s;

[0257] ④ Comparison of heat source before and after Dimensionless;

[0258] ⑤ Heat source expansion parameters The unit is mm;

[0259] ⑥ Fixture stiffness , unit N / mm.

[0260] The objective function is set as follows:

[0261] ① Maximum residual welding stress: Unit: MPa;

[0262] ② Maximum deformation after welding: , unit mm.

[0263] Step 2: Response Surface Design

[0264] The parameter space was sampled using the central composite design (CCD) method in response surface methodology to obtain several sets of parameter combination sample points. The sample points cover linear, interactive, and quadratic effect regions, exhibiting homogeneity and orthogonality.

[0265] Step 3: Finite Element Simulation Model Construction

[0266] Create a 3D thermo-mechanical coupling model on the Abaqus platform with the following settings:

[0267] (1) Material model: Considering the density as a function of temperature Thermal conductivity Specific heat capacity at constant pressure Coefficient of thermal expansion Elastic modulus Yield strength .

[0268] (2) Heat source model: The Goldak double ellipsoidal heat source model is adopted, and its volumetric heat flux density expression is:

[0269]

[0270] In the formula,

[0271] This is the transient volumetric heat flux density, in W / m³. 3 ;

[0272] The heat input power is expressed in watts (W), and the calculation formula is as follows:

[0273]

[0274] Thermal efficiency, which depends on the welding method and is dimensionless;

[0275] Welding voltage, unit: V;

[0276] Welding current, in amperes (A).

[0277] The semi-major axis of the heat source in the triaxial direction, in mm;

[0278] The ratio of the front / back heat source is... / , dimensionless, and satisfying the following relationship:

[0279]

[0280] (3) Thermal analysis: Solving the transient heat conduction equation:

[0281]

[0282] In the formula,

[0283] The density of the material is expressed in kg / m³.

[0284] This is the specific heat capacity at constant pressure of the material, expressed in J / (kg*K).

[0285] The thermal conductivity of the material is expressed in W / (m*K).

[0286] Temperature, in Kelvin (K).

[0287] This is the heat source term, with units of W / m³. 3 .

[0288] (4) Mechanical analysis: Based on the deformation and stress evolution calculation after thermal loading. A thermo-elastic-plastic constitutive model is adopted, and its formula is as follows:

[0289]

[0290] In the formula,

[0291] This is the stress tensor, with units of Pa.

[0292] This is the elastic stiffness tensor, with units of Pa.

[0293] The total strain tensor is dimensionless;

[0294] The coefficient of thermal expansion is 1 / K.

[0295] The initial temperature is expressed in Kelvin (K).

[0296] (5) Fixture modeling: Elastic supports are installed at the boundary nodes on both sides of the T-joint to simulate the function of the fixture. Its stiffness is measured using parameters. control.

[0297] Step 4: Batch Calculation and Result Extraction

[0298] All parameters are input into the Abaqus model, and a batch simulation is performed using a Python script. The simulation is completed automatically, and the following parameters are extracted:

[0299] The residual stress field yields the maximum principal stress. ;

[0300] Nodal displacement field, extracting the maximum displacement of the normal direction of the welded surface after welding. .

[0301] Output all simulation results to form a response surface modeling dataset.

[0302] Step 5: Response Surface Model Construction

[0303] Construct response surface models for the two objective functions respectively:

[0304]

[0305] in,

[0306] For predicting residual stress, the unit is MPa;

[0307] To predict the maximum deformation, the unit is mm;

[0308] Standardized values ​​for the parameters;

[0309] For the regression coefficients, the least squares method is used for fitting.

[0310] Step 6: Response Surface Optimization Solution

[0311] Optimization using a weighted method:

[0312]

[0313]

[0314] The optimal parameter combination is found by traversing the weight combinations and setting a target threshold. .

[0315] Step 7: Simulation Verification

[0316] Optimal parameters The simulation is applied to the original finite element model to re-simulate the welding process and verify whether the deviation between the predicted residual stress and deformation results and the actual simulation values ​​is within the allowable range. If it is satisfied, the optimization is successful; otherwise, a local augmentation experiment can be performed and the response surface updated.

[0317] Step 8: Process Output and Recommendations

[0318] The optimized process parameters are converted into welding process card content to guide actual T-joint welding operations, including:

[0319] Recommended welding current, voltage, and speed combinations;

[0320] Optimal heat source shape parameters (controlling the range of the molten pool);

[0321] Recommended fixture arrangement stiffness range;

[0322] Comprehensive recommendations for minimizing residual stress and controlling structural deformation.

[0323] In summary, the key technical points involved in the embodiments of the present invention are as follows:

[0324] ① Finite element simulation modeling and physical heat source description method for welding

[0325] A thermo-mechanical coupling simulation model was established using the Abaqus platform. The Goldak double ellipsoidal heat source model was adopted, and the heat input was finely loaded through the Fortran subroutine (DFlUX) to accurately reproduce the welding thermal cycle process and residual stress formation mechanism of complex structures.

[0326] ② Parameter-driven automated batch simulation system integration method

[0327] Develop Python control scripts to automate the processes of welding parameter input, batch model updates, calculation scheduling, result extraction and formatting, and streamline the entire process from parameter space sampling to simulation data generation.

[0328] ③ Response surface modeling method with multiple response variables

[0329] For multiple objective functions such as residual stress and post-weld deformation, a quadratic polynomial response surface model is established to fit the mapping relationship between simulation data and process parameters, supporting the simultaneous modeling of multiple performance indicators.

[0330] ④ Multi-objective optimization strategy based on response surface function

[0331] By employing the weighted sum method or goal programming method, multi-objective optimization can be performed directly on the constructed response surface, avoiding the use of computationally expensive methods such as genetic algorithms, thereby improving optimization efficiency and solution stability.

[0332] ⑤ Simulation-Optimization Coupled Verification and Closed-Loop Update Mechanism

[0333] Based on response surface prediction, simulation recalculation verification is performed, and an error tolerance judgment mechanism is set. If the error exceeds the set threshold, the augmented sampling process is automatically returned to achieve closed-loop optimization iteration.

[0334] ⑥ Applicability to the versatility and scalability of complex components in nuclear fusion devices

[0335] This method is applicable to welding structures of various nuclear fusion devices, such as vacuum chambers, cooling pipelines, and supporting flanges, and supports extension to multi-dimensional process decision-making scenarios such as sequence optimization and fixture design optimization.

[0336] In summary, the welding process parameter optimization method based on finite element simulation and response surface methodology of this invention integrates an automated closed-loop process of welding simulation modeling, response surface fitting, and multi-objective optimization. The method employs a double-ellipsoidal heat source model for heat source modeling and uses a user subroutine to control the distribution of moving heat sources. It establishes functional relationships between welding process parameters and multiple welding performance indicators (including but not limited to residual stress and post-weld deformation) using response surface methodology, thereby achieving multi-objective process optimization. The method uses a weighted sum method or goal programming to perform multi-objective optimization on the response surface model, avoiding computationally expensive evolutionary algorithms. It constructs a simulation verification feedback mechanism; when the response surface prediction error exceeds a preset tolerance, it automatically performs local sampling to update the response surface, improving the accuracy and robustness of the optimized solution. The method is applicable to residual stress and deformation control of welded structures in nuclear fusion devices and has scalability for other welding scenarios (such as aerospace and energy equipment).

[0337] In another aspect, the present invention also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method described above.

[0338] In another aspect, the present invention also discloses a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method described above.

[0339] It is understood that the systems, devices, and storage media provided in the embodiments of the present invention correspond to the methods provided in the embodiments of the present invention, and the explanations, examples, and beneficial effects of the relevant content can be referred to the corresponding parts of the above methods.

[0340] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0341] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0342] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0343] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing welding process parameters based on finite element simulation and response surface method, characterized in that, Comprising the following steps, S1, first according to the welding process characteristics, select the process parameters closely related to heat input and structural stiffness as design variables; And set the optimization objective function, clear optimization task input and output index; S2, based on the design variables and objective function determined in S1, use the central composite design in response surface method to generate representative parameter sample points; S3, use the finite element platform to establish a three-dimensional thermal-mechanical coupling model, and input the parameter combinations generated in S2 to form the corresponding simulation conditions. The output of the model is the temperature field, stress field and deformation result; S4, run the finite element model for all sample points generated in S2 in turn, and realize batch calculation and automatic data extraction through Python script; S5, import the input and output data obtained in S4 into the response surface modeling module, and establish a quadratic polynomial approximation function for residual stress and post-weld deformation respectively; S6, carry out optimization solution on the response surface function constructed in S5, and search for one or more optimal solutions that meet the performance balance requirements through weighted sum method or objective programming method optimization strategy, and form a Pareto solution set; S7, the candidate optimal solution obtained in S6 is re-input into the finite element model for verification calculation; S8, finally output the optimal process parameter combination that passes the verification, and apply it to the actual welding process card compilation, fixture design and welding sequence planning link, directly providing guidance for engineering practice.

2. The finite element simulation and response surface method based welding process parameter optimization method according to claim 1, characterized in that: S1 specifically includes, (1) determine the design variables, i.e. process parameters closely related to welding heat input and structural stiffness as follows: Arc current in A; Welding voltage in V; Welding speed in mm / s; heat source front-to-back ratio dimensionless; Heat source spread parameter in mm; Clamp stiffness in N / mm; (2) set two optimization objective functions: Welding residual stress maximum value: in MPa; Post-weld maximum deformation: in mm; Parameters Refers to the combination of welding process parameters, which is the input condition set that affects the welding residual stress and deformation results.

3. The finite element simulation and response surface method based welding process parameter optimization method according to claim 2, characterized in that: Step 2 specifically includes, An experiment scheme is constructed by using a central composite design in response surface method to generate 30 sample points in 4 parameter dimensions. An experiment scheme is constructed by using a central composite design in response surface method to generate 30 sample points in 4 parameter dimensions. An experiment scheme is constructed by using a central composite design in response surface method to Each sample point is a set of parameter combinations Corresponding to a simulation condition; Create *.inp input file automatically by Python script and set heat source parameters to realize simulation batch processing; n represents the number of design variables, i.e. the number of process parameters involved in optimization; N represents the total number of test sample points, i.e. the number of simulation conditions to be performed; represents the orthogonal combination point of all parameters, i.e. the cube vertex; representing the star point in the positive and negative direction of each parameter axis; c represents the number of central points, which is used to evaluate the simulation repeatability and model error; i represents the sample point number, i.e. the i-th parameter combination, corresponding to a specific welding condition combination.

4. The finite element simulation and response surface method based welding process parameter optimization method according to claim 3, characterized in that: Step 3 specifically includes, Establish a three-dimensional thermal-mechanical coupling model in Abaqus, and use a double-ellipsoid heat source model for heat input: In the formula, Volume heat flux density, W / m2, transient 3 ; The heat input power, in W, is calculated as follows: For thermal efficiency, dimensionless, depending on the welding form; V is the welding voltage, in V; For the welding current, the unit is A; L is the extended half-length of the heat source in the three-axis direction, in mm; For the front / back heat source ratio, i.e. / dimensionless, satisfying the following relationship: The heat conduction equation is: In the formula, Density of the material, in kg / m 3 ; Cp is the specific heat capacity at constant pressure of the material, in J / (kg*K); k is the thermal conductivity of the material, in W / (m*K); T is the temperature in K; W / m2K 3 ; After obtaining the temperature field, perform thermal deformation and stress evolution calculation; use the thermal elastic-plastic constitutive model, whose formula is as follows: In the formula, is the stress tensor, in Pa; is the elastic stiffness tensor, with units of Pa; E = total strain tensor, dimensionless; CTE is the coefficient of thermal expansion, in 1 / K; T0 is the initial temperature, in K.

5. The finite element simulation and response surface method based welding process parameter optimization method according to claim 4, characterized in that: Step 4 specifically includes, After running Abaqus analysis for each parameter combination, use Python script to automatically extract the following results: Residual stress maximum: ; Maximum displacement deformation: ; Peak temperature of thermal cycle, cooling rate; All results outputted as CSV, building data pairs ; represents the maximum welding residual stress calculated under the i-th combination of parameter groups, i.e. the stress peak in the simulation result, in MPa; represents the maximum deformation after welding under the i-th combination of parameter groups, i.e. the maximum displacement of the structure after welding is completed, in mm.

6. The finite element simulation and response surface method based welding process parameter optimization method according to claim 5, characterized in that: Step 5 specifically includes, Use a quadratic polynomial regression model to construct two objective functions respectively: Wherein, To predict the residual stress, units MPa; To predict the maximum deformation, in mm; is the parameter normalized value; For the regression coefficients, the least squares fit is used. The fit was evaluated using the coefficient of determination and the root mean square error RMSE, which requires ; k represents the target function number; Two optimization objectives: When k=1, f1(x) represents the maximum welding residual stress, unit: MPa; When k=2, f2(x) represents the maximum post-weld deformation, unit: mm; i, j: both represent the serial number of design variables, i.e. parameter number, and i≠j; That is, to identify each welding process parameter: When i / j=1, x1 is the arc current, unit: A; When i / j=2, x2 is the welding voltage, unit: V; When i / j=3, x3 is the welding speed, unit: mm / s; When i / j=4, x4 is the heat source front-to-back ratio, dimensionless; When i / j=5, x5 is the heat source spread parameter, unit: mm; When i / j=6, x6 is the fixture stiffness, unit: N / mm; Item represents the linear effect of each parameter on the outcome; Item represents the quadratic non-linear effect of the parameter; Item represents the interaction effect between parameters i and j.

7. The finite element simulation and response surface method based welding process parameter optimization method according to claim 6, characterized in that: Step 6 specifically includes, Two response surface optimization strategies are adopted as follows: Method A: Weighted sum method Construct the comprehensive objective function: For different weight combinations Optimization solver, search for minimum Forming the Pareto front; w1, w2: represent the weight coefficients of the two objective functions, used to reflect the importance of each objective; Both are dimensionless values and satisfy w1+w2=1; Method B: Goal programming method Given the maximum allowable stress and deformation: Take the sum of squared errors as the goal: obtaining an optimal parameter combination ; : indicates the maximum allowable residual stress limit, i.e. the upper limit allowed in the engineering design or material specification, in MPa; : indicates the maximum allowed deformation limit, i.e. the upper limit allowed in the structural assembly or tolerance requirements, in mm; : represents a target residual stress value desired to be achieved, unit: MPa; : represents the target deformation value desired to be reached, in mm.

8. The finite element simulation and response surface method based welding process parameter optimization method according to claim 7, characterized in that: Step 7 also includes, Combining the optimal parameters Input Abaqus model re-simulation, extract the actual Error analysis with predicted values: If the error is considered as optimization success; otherwise go back to step 2 for local augmented sampling; : represents the maximum value of welding residual stress obtained by finite element simulation, unit: MPa; : denotes the maximum deformation after welding by finite element simulation, unit: mm; : represents the relative error percentage of the kth objective function, i.e. the deviation between the predicted value and the actual simulation value.

9. The finite element simulation and response surface method based welding process parameter optimization method of claim 7, wherein: Step 8 further comprises outputting the final optimal parameter combination for guidance: Welding process card preparation; Fixture design and layout; Path planning and deformation countermeasures.

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