GPR-NSGA-II-based double-selective laser melting impact forging multi-target collaborative manufacturing optimization method

Abstract

The invention discloses a GPR-NSGA-II-based double-laser selective melting impact forging multi-target collaborative manufacturing optimization method, and the method comprises the steps: firstly carrying out the objective weighting of a plurality of targets, such as residual stress, deformation, residual stress depth, microstructure and density, through employing an entropy weight method based on the physical simulation data of double-laser impact forging; then, a Gaussian process regression (GPR) model is constructed, and the nonlinear relation between the technological parameters and the forming quality is accurately predicted; and in combination with an NSGA-II multi-objective optimization algorithm, a Pareto optimal solution set is solved. And finally, constructing a weighted objective function, screening out a globally optimal process parameter combination, and realizing collaborative optimization of the process parameters.

Description

Technical Field

[0001] This invention relates to additive manufacturing technology, and in particular to a multi-objective collaborative manufacturing optimization method based on GPR-NSGA-II dual-laser selective melting impact forging. Background Technology

[0002] With the development of my country's aerospace industry, complex structural components characterized by large size, integral construction, thin walls, and precision are increasingly being adopted. Currently, thin-walled complex structural components are generally manufactured using data processing methods, but the challenge of controlling deformation during processing is extremely prominent, making manufacturing very difficult. Therefore, adopting additive manufacturing methods for the integrated forming of complex structural components with large size, integral construction, thin walls, and precision is of great significance for expanding design boundaries, overcoming the limitations of traditional subtractive manufacturing, enabling the integrated forming of complex parts that cannot be processed by traditional processes, improving manufacturing efficiency and precision, shortening the R&D cycle, and promoting industrial upgrading.

[0003] Ensuring the reliability of component quality and the repeatability of manufacturing is the biggest challenge facing additive manufacturing, and it has been recognized as one of the obstacles restricting the development and industrial application of additive manufacturing technology. However, the mainstream selective laser melting additive parts currently available suffer from high thermal stress, defects, and insufficient fatigue performance, limiting their application in key load-bearing and moving parts. This has always been a technical problem and pain point for the industry.

[0004] The existing technology has the following technical problems: (1) Residual stress and deformation control of components. The temperature gradient and cooling rate in the existing additive manufacturing process are large, which easily leads to large thermal stress and uneven distribution of residual stress in the components, resulting in warping, cracking and dimensional deviation. (2) Formation of internal defects and unstable quality. Existing metal additive manufacturing components generally have internal defects such as porosity, lack of fusion and inclusions, resulting in insufficient component density and reduced fatigue life. (3) Anisotropy of microstructure and insufficient mechanical properties. In the traditional laser or electron beam melting process, columnar crystal structure is easily formed under rapid solidification, resulting in obvious directionality of mechanical properties. This invention achieves homogenization of microstructure and isotropic improvement of mechanical properties through process temperature field control and grain refinement mechanism. (4) Poor manufacturing repeatability and process controllability. Since the additive manufacturing process involves multi-physics field coupling (thermal field, stress field, flow field, etc.), the process parameters are sensitive to the results, resulting in performance fluctuations of components in the same batch. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a multi-objective collaborative manufacturing optimization method based on GPR-NSGA-II dual-laser selective melting impact forging. This method is a novel integrated additive manufacturing method or process system for large-scale, integral, thin-walled, and high-precision complex structural components. It enables the coordinated control of component thermal stress, microstructure evolution, and forming accuracy, fundamentally solving problems such as large deformation, numerous defects, and unstable performance of additively manufactured components. This ensures the reliability of component quality and the repeatability of the manufacturing process, providing technical support for the engineering application of key load-bearing components.

[0006] The objective of this invention is achieved through the following technical solutions.

[0007] A multi-objective collaborative manufacturing optimization method based on GPR-NSGA-II dual-laser selective melting impact forging includes the following steps:

[0008] 1) Based on the physical simulation data of dual-laser shock forging, the entropy weight method is used to objectively assign weights to five targets: residual stress f1, deformation f2, residual stress depth f3, microstructure f4, and density f5.

[0009] 2) Construct a Gaussian process regression model to accurately predict the nonlinear relationship between process parameters and forming quality;

[0010] 3) Combine non-dominated sorting genetic algorithm for multi-objective optimization to find the Pareto optimal solution set;

[0011] 4) Construct a weighted objective function, select the globally optimal combination of process parameters, and achieve collaborative optimization of process parameters.

[0012] Step 1) specifically includes the following steps: 1.1) Data preparation: Through a physical simulation model, obtain specific values ​​of residual stress magnitude, deformation degree, residual stress depth, microstructure, and density under different conditions of temperature, impact energy, pulse width, pulse frequency, radius, and overlapping radius areas during impact forging; clean the data, including imputation of missing values ​​and removal of duplicate data; normalize the data to eliminate the influence of dimensions.

[0013] For minimization indices, the following normalization formula is used:

[0014]

[0015] x ij : Normalized data values;

[0016] y ij : Original data value;

[0017] min k y kjThe minimum value of the j-th target variable across all samples;

[0018] max k y kj The maximum value of the j-th target variable across all samples;

[0019] N: Total number of samples;

[0020] The normalized matrix X = [x ij ];

[0021] 1.2) Entropy weight method to determine weights: Calculate the weight of the i-th sample on the j-th indicator:

[0022]

[0023] Calculate the entropy value of the j-th index:

[0024]

[0025] Calculate the coefficient of variation:

[0026] d j =1-e j ;

[0027] Determine objective weights:

[0028]

[0029] W j The weight of the j-th indicator;

[0030] d j The coefficient of difference for the j-th indicator;

[0031] The sum of the differences of all indicators;

[0032] The final weights for residual stress, deformation, residual stress depth, microstructure, and density are w1, w2, w3, w4, and w5, respectively, satisfying ∑W j =1, this weight will be used for the comprehensive evaluation of the Pareto solution set in the future.

[0033] Step 2) specifically includes the following steps: 2.1) Data preparation: Obtain a dataset of input parameters and target variables through physical simulation. The input parameters include temperature, impact energy, pulse width, pulse frequency, radius, and radius overlap region. The target variables include residual stress magnitude, deformation, residual stress depth, microstructure, and density. The input parameters and target variables are normalized to eliminate the influence of dimensions. The processed dataset is divided into a training set and a test set in a 7:3 ratio for subsequent model training and evaluation.

[0034] 2.2) Define the kernel function: Use cross-validation to evaluate the prediction accuracy of different kernel functions and select the best one as the kernel function of the final model: Evaluate each candidate kernel function through K-fold cross-validation: Divide the training set into K subsets, use K-1 subsets for training each time, and use the remaining subset for validation. Repeat this K times, calculate the average prediction error, evaluate the performance of each kernel function through K-fold cross-validation, and select the kernel function with the smallest root mean square error and the highest coefficient of determination as the optimal kernel function;

[0035] 2.3) Training Gaussian process regression model: Using the Gaussian process regression method, prediction models are established with temperature, impact energy, pulse width, pulse frequency, radius and radius overlap area as inputs, and residual stress magnitude, deformation, residual stress depth, microstructure and density as outputs.

[0036] 2.4) Model Prediction and Evaluation: After completing the model training, the predictive performance of the GPR model is evaluated using the test set. The root mean square error, mean absolute error, and coefficient of determination are calculated to evaluate the effectiveness and reliability of the GPR model.

[0037] The specific steps of step 3) include: 3.1) Defining the objective function: The objective function should be defined as a vector objective function Minimize: F(X)=[f1(X),f2(X),f3(X),f4(X),f5(X)], X=[T,E,τ,f,R,R_overlap] is a process parameter vector, which respectively represent temperature, impact energy, pulse width, pulse frequency, radius and radius overlap area;

[0038] f1(X) is the predicted value of residual stress, f2(X) is the predicted value of deformation, f3(X) is the predicted value of residual stress depth, f4(X) is the predicted value of microstructure, and f5(X) is the predicted value of density. All of the above predicted values ​​are provided by the Gaussian process regression model.

[0039] Each process parameter is limited by equipment capacity and process window, and the following boundary constraints are set:

[0040] T∈[T min ,T max ]

[0041] E∈[E min E max ]

[0042] τ∈[τ min ,τ max ]

[0043] f∈[f min ,fmax ]

[0044] R∈[R min ,R max ]

[0045] R overlap ∈[R overlap,min ,r overlap,max ];

[0046] 3.2) Optimization is achieved using a non-dominated sorting genetic algorithm: By simulating the processes of natural selection and genetic mutation, a set of optimal solutions is gradually evolved, including the following steps:

[0047] 3.2.1) Initialize the population: Randomly generate initial solutions within the boundaries of the process parameters;

[0048] 3.2.2) Fitness assessment: The individual is assessed using a target function;

[0049] 3.2.3) Selection Operation: A tournament selection method is used to screen outstanding individuals;

[0050] 3.2.4) Crossover and Mutation: Offspring are generated by simulating binary crossover and polynomial mutation;

[0051] 3.2.5) Non-dominated ordination and crowding distance calculation: stratifying the population while maintaining diversity;

[0052] 3.2.6) Elite Preservation Strategy: Merge parent and offspring generations, and select the best individual to enter the next generation;

[0053] 3.2.7) Termination condition determination: Stop when the maximum number of iterations is reached or the solution set converges;

[0054] The range of process parameters is set as a constraint condition for the optimization variable. A non-dominated sorting genetic algorithm is used to search in the solution space, and finally a set of Pareto optimal solutions is obtained.

[0055] Step 4) uses the weights w1, w2, w3, w4, w5 of each objective parameter determined by the entropy weight method to construct a weighted sum objective function:

[0056] S(X)=W1·f1(X)+W2·f2(X)+W3·f3(X)+W4·f4(X)+W5·(1-f5(X))

[0057] The solution that minimizes S(X) is selected as the final recommended optimal combination of process parameters.

[0058] Finite element analysis of dual-laser selective melting impact forging, the specific steps of which include:

[0059] a) Establish a simulation model of dual-laser coupled forming-impact forging.

[0060] Based on the characteristics of the selective melting process, the model geometry and boundary conditions are simplified; the matrix and cladding materials adopt the same physical properties, the model defines the layer thickness in the Z direction and the scanning path in the XY plane; by applying convection and radiation boundary conditions, a transient thermo-mechanical coupling analysis model is constructed.

[0061] b) Finite element meshing and element property definition

[0062] A three-dimensional thermo-mechanical coupled element type suitable for high-temperature nonlinear deformation is adopted. The temperature-dependent parameters of the material are defined, including density ρ(T), specific heat capacity c(T), thermal conductivity λ(T), elastic modulus E(T), Poisson's ratio μ(T), and yield stress σy(T). The Johnson-Cook constitutive model is introduced to describe the plastic behavior under high strain rate.

[0063] c) Simulation of the melting and forming process

[0064] Transient thermal analysis model: The temperature field distribution under laser irradiation is calculated by establishing a nonlinear transient heat conduction equation;

[0065] Laser heat source model: A Gaussian surface heat source is used to describe the laser energy distribution in selected melting.

[0066] The birth-death unit method: Employs a layer-by-layer activation strategy to simulate the gradual melting, solidification, and stacking process of powder layers;

[0067] Parameter scanning: Simulate different laser powers, scanning speeds and spot radii, and output temperature field data that satisfies the stability of the molten pool.

[0068] d) Temperature field-impact forging coupling

[0069] The transient temperature field data obtained during the melting and forming stage is used as the initial condition and imported into the impact analysis module to achieve thermo-mechanical coupling solution; the element in the "suitable forging temperature zone" is selected as the impact target within the temperature range;

[0070] e) Laser shock load modeling

[0071] Shock wave model: using Gaussian pulse pressure function

[0072] P(t)=P max exp[-(t / τ) 2 ]

[0073] Where Pmax is the peak pressure, τ is the pulse width, and t is the time from the start of the pulse.

[0074] Spatial distribution: Apply a Gaussian surface distribution on the XY plane;

[0075] Scan trajectory: Dynamically load along the selected path, and set the pulse overlap rate and scan speed;

[0076] Loading method: Multi-pulse loading is implemented using the VDLOAD subroutine to simulate the time-space evolution of impact forging;

[0077] f) Impact forging simulation and stress evolution analysis

[0078] Temperature-stress coupling: Calculating stress wave propagation and plastic deformation under impact;

[0079] Results output: Residual stress distribution, plastic strain contour map, and impact influence depth;

[0080] Optimization analysis: By combining different peak pressures, pulse widths, and scanning speeds, the process window for stress relaxation, pore closure, and the absence of new cracks was determined.

[0081] g) Collaborative optimization and parameter feedback

[0082] Based on simulation data, a reasonable forging temperature range and optimal impact window are extracted, and the timing and spatial spacing between the two lasers are optimized.

[0083] If the forging window is delayed, reduce the forging laser delay;

[0084] If the depth or width of the molten pool exceeds the reference value by 15%, adjust the laser power or scanning rate.

[0085] If the peak residual tensile stress exceeds 50% of the material's yield strength, adjust the peak pressure or pulse frequency;

[0086] The optimal coupling parameter set for the "melting-impact" dual laser was finally determined.

[0087] h) Process visualization

[0088] The simulation results are visualized and output, including the dynamic changes of temperature field, stress field and forging area over time, forming an optimization parameter database.

[0089] Compared to existing technologies, the advantages of this invention are as follows: This invention achieves balanced thermal stress distribution and stable component forming by optimizing heat input control, path planning, and process regulation. This invention effectively suppresses defect formation and improves microstructure density and quality consistency by improving material powder spreading characteristics, energy field control, and multi-layer molten pool synergy mechanisms. This invention achieves homogenization of microstructure and isotropic improvement of mechanical properties through process temperature field regulation and grain refinement mechanisms. This invention improves the stability and repeatability of the manufacturing process by introducing process monitoring and closed-loop control methods. Attached Figure Description

[0090] Figure 1 This is a schematic diagram of the finite element analysis of dual-laser selective melting impact forging according to the present invention.

[0091] Figure 2 This is a flowchart of the multi-target collaborative manufacturing optimization process based on GPR-NSGA-II dual-laser selective melting impact forging. Detailed Implementation

[0092] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0093] Finite element analysis of dual-laser selective melting-impact forging

[0094] To address issues such as thermal stress concentration, microstructure coarsening, and residual tensile stress during dual-laser selective melting forming, this invention proposes a synergistic control and optimization method for dual-laser selective melting and impact forging based on finite element simulation. This method comprehensively considers the laser-thermal-mechanical coupling effect in a numerical simulation environment and achieves synergistic optimization of the forming process and the impact forging stage through multiphysics modeling. Figure 1 As shown.

[0095] Includes the following steps:

[0096] (1) Establish a simulation model of dual laser coupling forming-impact forging

[0097] Based on the characteristics of the selective melting process, the model geometry and boundary conditions are simplified. The matrix and cladding materials use the same physical properties. The model defines the layer thickness in the Z direction and the scanning path in the XY plane. A transient thermo-mechanical coupling analysis model is constructed by applying convection and radiation boundary conditions.

[0098] (2) Finite element meshing and element property definition

[0099] A three-dimensional thermo-mechanical coupling element type suitable for high-temperature nonlinear deformation (such as C3D8RT) is adopted.

[0100] Temperature-dependent parameters of the material are defined, including density ρ(T), specific heat capacity c(T), thermal conductivity λ(T), elastic modulus E(T), Poisson's ratio μ(T), yield stress σy(T), etc., and the Johnson-Cook constitutive model is introduced to describe the plastic behavior under high strain rates.

[0101] (3) Simulation of melting and forming process

[0102] Transient thermal analysis model: The temperature field distribution under laser irradiation is calculated by establishing a nonlinear transient heat conduction equation;

[0103] Laser heat source model: A Gaussian surface heat source is used to describe the laser energy distribution in selected melting.

[0104] The birth-death unit method: Employs a layer-by-layer activation strategy to simulate the gradual melting, solidification, and stacking process of powder layers;

[0105] Parameter scanning: Simulate different laser powers, scanning speeds and spot radii, and output temperature field data that satisfies the stability of the molten pool.

[0106] (4) Temperature field-impact field coupling

[0107] The transient temperature field data obtained during the melting and forming stage is imported into the impact analysis module as initial conditions to achieve thermo-mechanical coupling solution. Elements within the "suitable forging temperature zone" are selected as impact targets within the temperature range.

[0108] (5) Modeling of laser shock load

[0109] P(t)=P max exp[-(t / τ) 2 ]

[0110] Shock wave model: using Gaussian pulse pressure function

[0111] Where Pmax is the peak pressure, τ is the pulse width, and t is the time from the start of the pulse.

[0112] Spatial distribution: Apply a Gaussian surface distribution on the XY plane;

[0113] Scan trajectory: Dynamically load along the selected path, and set the pulse overlap rate and scan speed;

[0114] Loading method: Multi-pulse loading is implemented using the VDLOAD subroutine to simulate the time-space evolution of impact forging.

[0115] (6) Impact forging simulation and stress evolution analysis

[0116] Temperature-stress coupling: Calculating stress wave propagation and plastic deformation under impact;

[0117] Results output: Residual stress distribution, plastic strain contour map, and impact influence depth;

[0118] Optimization analysis: By combining different peak pressures, pulse widths, and scanning speeds, the process window for stress relaxation, pore closure, and the absence of new cracks is determined.

[0119] (7) Collaborative optimization and parameter feedback

[0120] Based on simulation data, a reasonable forging temperature range and optimal impact window are extracted, and the timing and spatial spacing between the two lasers are optimized: if the forging window is lagging, the forging laser delay is reduced.

[0121] If the depth or width of the molten pool exceeds the reference value by 15%, adjust the laser power or scanning rate.

[0122] If the peak residual tensile stress exceeds 50% of the material's yield strength, adjust the peak pressure or pulse frequency;

[0123] The optimal coupling parameter set for the "melting-impact" dual laser was finally determined.

[0124] (8) Process visualization

[0125] The simulation results are visualized and output, including the dynamic changes of temperature field, stress field and forging area over time, forming an optimization parameter database.

[0126] Based on physical simulation data of dual-laser shock forging, the entropy weight method is first used to objectively assign weights to multiple objectives, including residual stress, deformation, residual stress depth, microstructure, and density. Then, a Gaussian process regression (GPR) model is constructed to accurately predict the nonlinear relationship between process parameters and forming quality. Combined with the NSGA-II multi-objective optimization algorithm, the Pareto optimal solution set is obtained. Finally, a weighted objective function is constructed to select the globally optimal combination of process parameters, achieving synergistic optimization of process parameters. The optimization scheme is as follows: Figure 2 As shown.

[0127] 1. Problem Definition and Target Parameter Weight Setting

[0128] This invention aims to address the interdependent relationship between multiple objectives, including residual stress, deformation, and residual stress depth, in metal additive manufacturing, thereby achieving synergistic optimization of forming quality. In metal additive manufacturing, residual stress, deformation, residual stress depth, microstructure, and density are key factors affecting forming quality. During impact forging, a complex relationship exists among residual stress, deformation, residual stress depth, microstructure, and density. Residual stress is the primary factor inducing deformation; the greater the residual stress, the higher the probability of deformation. Furthermore, the depth of residual stress directly determines whether the deformation extends throughout the entire part or is limited to the surface.

[0129] To achieve synergistic optimization of these multiple objectives, this paper selects residual stress (f1), deformation (f2), residual stress depth (f3), microstructure (f4), and density (f5) as optimization targets. Meanwhile, to avoid bias caused by subjective weighting, this paper employs the entropy weight method to objectively determine the weights of each objective.

[0130] (1) Data preparation

[0131] Using a physical simulation model, specific values ​​were obtained for residual stress magnitude, deformation degree, residual stress depth, microstructure, and density during impact forging under different conditions including temperature, impact energy, pulse width, pulse frequency, radius, and overlapping radius regions. Subsequently, the data was cleaned, including imputation of missing values ​​and removal of duplicate data. Furthermore, the data was normalized to eliminate the influence of dimensions.

[0132] For minimization indices, the following normalization formula is used:

[0133]

[0134] x ij : Normalized data values;

[0135] y ij : Original data value;

[0136] min k y kj The minimum value of the j-th target variable across all samples;

[0137] max k y kj The maximum value of the j-th target variable across all samples;

[0138] N: Total number of samples;

[0139] The normalized matrix X = [x ij ].

[0140] (2) Determining weights using the entropy weight method

[0141] ① Calculate the weight of the i-th sample on the j-th indicator:

[0142]

[0143] ② Calculate the entropy value of the j-th index:

[0144]

[0145] ③ Calculate the coefficient of variation:

[0146] d j =1-e j

[0147] ④ Determine objective weights:

[0148]

[0149] W j The weight of the j-th indicator;

[0150] dj The coefficient of difference for the j-th indicator;

[0151] The sum of the differences of all indicators;

[0152] The final weights for residual stress, deformation, residual stress depth, microstructure, and density are w1, w2, w3, w4, and w5, respectively, satisfying ∑W j =1. This weight will be used for the comprehensive evaluation of the subsequent Pareto solution set.

[0153] 2. Establish a prediction model

[0154] (1) Data preparation

[0155] A dataset containing input parameters (temperature, impact energy, pulse width, pulse frequency, radius, and radius overlap region) and target variables (residual stress, deformation, residual stress depth, microstructure, and density) was obtained through physical simulation and then standardized. Standardization included handling missing values ​​and detecting and removing outliers. Subsequently, the processed dataset was divided into training and testing sets in a 7:3 ratio for subsequent model training and evaluation.

[0156] (2) Define kernel function

[0157] The choice of kernel function has a crucial impact on the predictive performance of Gaussian Process Regression (GPR) models. Commonly used kernel functions include radial basis functions (RBF), Matérn kernels, and multinomial kernels. This study employs cross-validation to evaluate the prediction accuracy of different kernel functions and selects the optimal one as the kernel function for the final model. Specifically, each candidate kernel function is evaluated using K-fold cross-validation: the training set is further divided into K subsets, and K-1 subsets are used for training each time, with the remaining subset used for validation. This process is repeated K times, and the average prediction error (e.g., root mean square error RMSE, coefficient of determination R0) is calculated. 2 (etc.). The performance of each kernel function was evaluated using K-fold cross-validation, and the kernel with the smallest root mean square error (RMSE) and the lowest coefficient of determination (R²) was selected. 2 The kernel function with the highest value is taken as the optimal kernel function.

[0158] (3) Training the Gaussian process regression model

[0159] The Gaussian Process Regression (GPR) method was used to establish prediction models with temperature, impact energy, pulse width, pulse frequency, radius, and radius overlap region as inputs, and residual stress magnitude, deformation, residual stress depth, microstructure, and density as outputs.

[0160] (4) Model prediction and evaluation

[0161] After completing model training, the predictive performance of the GPR model is evaluated using a test set. The root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) are calculated. 2 The effectiveness and reliability of the GPR model are tested using evaluation indicators such as (e.g., [missing information]).

[0162] 3. Multi-objective optimization

[0163] (1) Define the objective function

[0164] The objective function should be defined as a vector objective function.

[0165] Minimize: F(X)=[f1(X),f2(X),f3(X),f4(X),f5(X)]

[0166] X = [T, E, τ, f, R, R_overlap] is a vector of process parameters, representing temperature, impact energy, pulse width, pulse frequency, radius, and the radius overlap region, respectively.

[0167] f1(X) is the predicted value of residual stress, f2(X) is the predicted value of deformation, f3(X) is the predicted value of residual stress depth, f4(X) is the predicted value of microstructure, and f5(X) is the predicted value of density. These predictions are all provided by the Gaussian process regression (GPR) model.

[0168] Each process parameter is limited by equipment capacity and process window, and the following boundary constraints are set:

[0169] T∈[T min ,T max ]

[0170] E∈[E min E max ]

[0171] τ∈[τ min ,τ max ]

[0172] f∈[f min ,f max ]

[0173] R∈[R min,R max ]

[0174] R overlap ∈[R overlap,min ,R overlap,max ]

[0175] (2) The non-dominated sorting genetic algorithm (NSGA-II) is used for optimization.

[0176] The Non-Dominated Sorting Genetic Algorithm (NSGA-II) is a commonly used multi-objective optimization algorithm that can effectively solve optimization problems with multiple conflicting objectives. It evolves a set of optimal solutions step-by-step by simulating the processes of natural selection and genetic mutation. The steps include:

[0177] (1) Initialize the population: Randomly generate initial solutions within the boundaries of the process parameters;

[0178] (2) Fitness assessment: The objective function is used to assess the individual;

[0179] (3) Selection process: The tournament selection method is used to screen outstanding individuals;

[0180] (4) Crossover and mutation: Offspring are generated by simulating binary crossover (SBX) and polynomial mutation;

[0181] (5) Non-dominated ordering and crowding distance calculation: stratify the population and maintain diversity;

[0182] (6) Elite preservation strategy: merge the parent generation and the offspring generation, and select the best individual to enter the next generation;

[0183] (7) Termination condition judgment: Stop when the maximum number of iterations is reached or the solution set converges.

[0184] The range of process parameters was set as a constraint on the optimization variables. A non-dominated sorting genetic algorithm (NSGA-II) was used to search the solution space, ultimately obtaining a Pareto optimal set. This set, under the given constraints, represents the optimal trade-off between residual stress, deformation, residual stress depth, microstructure, and density, where further simultaneous optimization is not possible.

[0185] Finally, using the weights w1, w2, w3, w4, and w5 of each objective parameter determined by the entropy weight method, a weighted sum objective function is constructed:

[0186] S(X)=W1·f1(X)+W2·f2(X)+W3·f3(X)+W4·f4(X)+W5·(1-f5(X))

[0187] The solution that minimizes S(X) is selected as the final recommended optimal combination of process parameters.

[0188] This invention constructs a closed-loop process parameter optimization method for dual-laser shock forging additive manufacturing, employing a "data-driven—objective weighting—intelligent optimization" approach. This method effectively overcomes the limitations of traditional process optimization methods that rely on empirical trial and error and single-objective optimization. In the modeling stage, Gaussian process regression (GPR) is introduced for performance prediction of the dual-laser shock forging additive manufacturing process. Based on limited physical simulation data, the GPR model can accurately fit the nonlinear mapping relationship between process parameters and forming quality indicators (including residual stress, deformation, residual stress depth, microstructure, and density), and simultaneously outputs an uncertainty measure of the prediction results. This provides support for evaluating the reliability of model predictions and quantifying uncertainty, making it particularly suitable for advanced manufacturing scenarios such as laser shock forging where experimental costs are high and sample acquisition is difficult.

[0189] In terms of multi-objective weight allocation, the entropy weight method is adopted. Based on the information entropy differences of each objective index in the simulation data, the objective weights of residual stress, deformation, residual stress depth, microstructure, and density are automatically calculated, avoiding subjective biases introduced by manual weighting and improving the scientific nature and repeatability of the optimization results. Furthermore, a "GPR+NSGA-II" collaborative optimization architecture is constructed: a Gaussian process regression (GPR) model is used as a surrogate model to replace time-consuming physical simulation for rapid prediction of forming quality indicators corresponding to process parameters; combined with the NSGA-II multi-objective genetic algorithm, the Pareto optimal solution set is efficiently solved under process constraints. The system presents the trade-off relationship between residual stress, deformation, and residual stress depth, and improves global search capabilities.

[0190] By establishing a closed-loop optimization process of "physical simulation → data modeling → multi-objective optimization → simulation verification," the reliance on physical experiments is effectively reduced, lowering material consumption, time costs, and equipment occupancy, while improving the efficiency and reliability of additive manufacturing process parameter development. This invention is applicable to the optimization of additive manufacturing process parameters for various metal materials and complex structural components, such as titanium alloys, nickel-based superalloys, and aluminum alloys. For different material systems, only retraining the GPR model based on corresponding physical simulation or experimental data is required to achieve prediction and multi-objective optimization of key indicators such as residual stress and deformation, demonstrating good adaptability. Compared to traditional methods that rely on experience-based trial and error or single-objective optimization, this solution combines data-driven modeling with intelligent optimization, which can provide synergistic optimization results for multiple performance indicators while reducing the number of physical experiments, thus helping to improve process development efficiency and consistency.

Claims

1. A multi-objective collaborative manufacturing optimization method based on GPR-NSGA-II dual-laser selective melting impact forging, characterized by the following steps include: 1) Based on the physical simulation data of dual laser shock forging, the entropy weight method is used to objectively assign weights to five targets: residual stress f1, deformation f2, residual stress depth f3, microstructure f4, and density f5. 2) Construct a Gaussian process regression model to accurately predict the nonlinear relationship between process parameters and forming quality; 3) Combine non-dominated sorting genetic algorithm for multi-objective optimization to find the Pareto optimal solution set; 4) Construct a weighted objective function, select the globally optimal combination of process parameters, and achieve collaborative optimization of process parameters.

2. The multi-objective collaborative manufacturing optimization method based on GPR-NSGA-II dual-laser selective melting impact forging as described in claim 1, characterized in that... Step 1) specifically includes the following steps: 1.1) Data preparation: Through a physical simulation model, obtain specific values ​​for residual stress magnitude, deformation degree, residual stress depth, microstructure, and density under different conditions of temperature, impact energy, pulse width, pulse frequency, radius, and overlapping radius areas during impact forging; clean the data, including imputation of missing values ​​and removal of duplicate data; normalize the data to eliminate the influence of dimensions: for minimization indicators, the following normalization formula is used: x ij : Normalized data values; y ij : Original data value; min k y kj The minimum value of the j-th target variable across all samples; max k y kj The maximum value of the j-th target variable across all samples; N: Total number of samples; The normalized matrix X = [x ij ].; 1.2) Entropy weight method to determine weights: Calculate the weight of the i-th sample on the j-th indicator: Calculate the entropy value of the j-th index: Calculate the coefficient of variation: d j =1-e j ; Determine objective weights: W j The weight of the j-th indicator; d j The coefficient of difference for the j-th indicator; The sum of the differences of all indicators; The final weights for residual stress, deformation, residual stress depth, microstructure, and density are w1, w2, w3, w4, and w5, respectively, satisfying ∑W j =1, this weight will be used for the comprehensive evaluation of the Pareto solution set in the future.

3. The multi-objective collaborative manufacturing optimization method based on GPR-NSGA-II dual-laser selective melting impact forging as described in claim 2, characterized in that... Step 2) specifically includes the following steps: 2.1) Data preparation: Obtain a dataset of input parameters and target variables through physical simulation. The input parameters include temperature, impact energy, pulse width, pulse frequency, radius, and radius overlap region. The target variables include residual stress magnitude, deformation, residual stress depth, microstructure, and density. The input parameters and target variables are normalized to eliminate the influence of dimensions. The processed dataset is divided into a training set and a test set in a 7:3 ratio for subsequent model training and evaluation. 2.2) Define the kernel function: Use cross-validation to evaluate the prediction accuracy of different kernel functions and select the best one as the kernel function of the final model: Evaluate each candidate kernel function through K-fold cross-validation: Divide the training set into K subsets, use K-1 subsets for training each time, and use the remaining subset for validation. Repeat this process K times, calculate the average prediction error, evaluate the performance of each kernel function through K-fold cross-validation, and select the kernel function with the smallest root mean square error and the highest coefficient of determination as the optimal kernel function; 2.3) Training Gaussian process regression model: Using the Gaussian process regression method, prediction models are established with temperature, impact energy, pulse width, pulse frequency, radius and radius overlap area as inputs, and residual stress magnitude, deformation, residual stress depth, microstructure and density as outputs. 2.4) Model Prediction and Evaluation: After completing the model training, the predictive performance of the GPR model is evaluated using the test set. The root mean square error, mean absolute error, and coefficient of determination are calculated to evaluate the effectiveness and reliability of the GPR model.

4. The multi-objective collaborative manufacturing optimization method based on GPR-NSGA-II dual-laser selective melting impact forging as described in claim 3, characterized in that... Step 3) specifically includes the following steps: 3.1) Define the objective function: The objective function should be defined as a vector objective function Minimize: F(X)=[f1(X), f2(X), f3(X), f4(X), f5(X)], X=[T,E,τ,f,R,R_overlap] is a process parameter vector, representing temperature, impact energy, pulse width, pulse frequency, radius and radius overlap area respectively; f1(X) is the predicted value of residual stress, f2(X) is the predicted value of deformation, f3(X) is the predicted value of residual stress depth, f4(X) is the predicted value of microstructure, and f5(X) is the predicted value of density. All the above predicted values ​​are provided by the Gaussian process regression model; Each process parameter is limited by equipment capacity and process window, and the following boundary constraints are set: T∈[T min ,T max ] E∈[E min ,AND max ] τ∈[τ min ,T max ] f∈[f min ,f max ] R∈[R min ,R max ] R overlap ∈[R overlap，min ,R overlap,max ]; 3.2) Optimization is achieved using a non-dominated sorting genetic algorithm: By simulating the processes of natural selection and genetic mutation, a set of optimal solutions is gradually evolved, including the following steps: 3.2.1) Initialize the population: Randomly generate initial solutions within the boundaries of the process parameters; 3.2.2) Fitness assessment: The individual is assessed using a target function; 3.2.3) Selection Operation: A tournament selection method is used to screen outstanding individuals; 3.2.4) Crossover and Mutation: Offspring are generated by simulating binary crossover and polynomial mutation; 3.2.5) Non-dominated ordination and crowding distance calculation: stratifying the population while maintaining diversity; 3.2.6) Elite Preservation Strategy: Merge parent and offspring generations, and select the best individual to enter the next generation; 3.2.7) Termination condition determination: Stop when the maximum number of iterations is reached or the solution set converges; The range of process parameters is set as a constraint condition for the optimization variable. A non-dominated sorting genetic algorithm is used to search in the solution space, and finally a set of Pareto optimal solutions is obtained.

5. The multi-objective collaborative manufacturing optimization method based on GPR-NSGA-II dual-laser selective melting impact forging as described in claim 4, characterized in that... Step 4) uses the weights w1, w2, w3, w4, w5 of each objective parameter determined by the entropy weight method to construct a weighted sum objective function: S(X)=W1·f1(X)+W2·f2(X)+W3·f3(X)+W4·f4(X)+W5·(1-f5(X)) The solution that minimizes S(X) is selected as the final recommended optimal combination of process parameters.

6. The multi-objective collaborative manufacturing optimization method based on GPR-NSGA-II dual-laser selective melting impact forging as described in claim 4, characterized in that... It also includes finite element analysis of dual-laser selective melting impact forging, the specific steps of which include: a) Establish a simulation model of dual-laser coupled forming-impact forging. Based on the characteristics of the selective melting process, the model geometry and boundary conditions are simplified; the matrix and cladding materials adopt the same physical properties, the model defines the layer thickness in the Z direction and the scanning path in the XY plane; by applying convection and radiation boundary conditions, a transient thermo-mechanical coupling analysis model is constructed. b) Finite element meshing and element property definition A three-dimensional thermo-mechanical coupled element type suitable for high-temperature nonlinear deformation is adopted. The temperature-dependent parameters of the material are defined, including density ρ(T), specific heat capacity c(T), thermal conductivity λ(T), elastic modulus E(T), Poisson's ratio μ(T), and yield stress σy(T). The Johnson-Cook constitutive model is introduced to describe the plastic behavior under high strain rate. c) Simulation of the melting and forming process Transient thermal analysis model: The temperature field distribution under laser irradiation is calculated by establishing a nonlinear transient heat conduction equation; Laser heat source model: A Gaussian surface heat source is used to describe the laser energy distribution in selected melting. The birth-death unit method: Employs a layer-by-layer activation strategy to simulate the gradual melting, solidification, and stacking process of powder layers; Parameter scanning: Simulates different laser powers, scanning speeds and spot radii, and outputs temperature field data that ensures the stability of the molten pool. d) Temperature field-impact forging coupling The transient temperature field data obtained during the melting and forming stage is used as the initial condition and imported into the impact analysis module to achieve thermo-mechanical coupling solution; the element in the "suitable forging temperature zone" is selected as the impact target within the temperature range; e) Laser shock forging load modeling Shock wave model: using Gaussian pulse pressure function P(t)=P max exp[-(t / τ) 2 ] Where Pmax is the peak pressure, τ is the pulse width, and t is the time from the start of the pulse. Spatial distribution: Apply a Gaussian surface distribution on the XY plane; Scan trajectory: Dynamically load along the selected path, and set the pulse overlap rate and scan speed; Loading method: Multi-pulse loading is implemented using the VDLOAD subroutine to simulate the time-space evolution of impact forging; f) Impact forging simulation and stress evolution analysis Temperature-stress coupling: Calculating stress wave propagation and plastic deformation under impact; Results output: Residual stress distribution, plastic strain contour map, and impact influence depth; Optimization analysis: By combining different peak pressures, pulse widths, and scanning speeds, the process window for stress relaxation, pore closure, and the absence of new cracks was determined. g) Collaborative optimization and parameter feedback Based on simulation data, a reasonable forging temperature range and optimal impact window are extracted, and the timing and spatial spacing between the two lasers are optimized: if the forging window is lagging, the forging laser delay is reduced. If the depth or width of the molten pool exceeds the reference value by 15%, adjust the laser power or scanning rate. If the peak residual tensile stress exceeds 50% of the material's yield strength, adjust the peak pressure or pulse frequency; The optimal coupling parameter set for the "melting-impact forging" dual laser was finally determined. h) Process visualization The simulation results are visualized and output, including the dynamic changes of temperature field, stress field and forging area over time, forming an optimization parameter database.

Images