Multi-objective performance collaborative optimization method of laser powder bed melting process for topological optimization body-centered cubic lattice structure

Abstract

The invention relates to a topological optimization body-centered cubic lattice structure-oriented multi-objective performance collaborative optimization method for a laser powder bed melting process, and belongs to the field of metal additive manufacturing. In order to solve the problems that a T-BCC lattice structure is large in residual stress, the structure is difficult to accurately regulate and control and rigidity and energy absorption are difficult to consider in selective laser melting forming, laser power, scanning speed and powder laying thickness are used as design variables, a thermal-force finite element and a grain evolution phase field model are coupled, residual stress and grain size characteristics are obtained, and a T-BCC lattice structure is obtained. Training a multi-output random forest process-organization-performance agent model in combination with experimental data; under the manufacturability constraint, a multi-objective evolutionary algorithm is introduced to solve a Pareto solution set of residual stress, equivalent Young modulus and unit volume energy absorption, a T-BCC dot matrix LPBF high-performance process window is constructed, and rapid recommendation of process parameters is realized. And the test cost is remarkably reduced, the service reliability of the lattice component is improved, and important engineering application value is achieved.

Description

Technical Field

[0001] This invention relates to a multi-objective performance synergistic optimization method for laser powder bed melting process for topology-optimized body-centered cubic lattice structures, belonging to the field of metal additive manufacturing. Background Technology

[0002] Metal additive manufacturing technology, characterized by layer-by-layer deposition and rapid metallurgical solidification, enables metal components to break free from the geometric limitations of traditional processing, demonstrating significant advantages in the fabrication of lightweight structures, energy-absorbing structures, and complex functionally graded structures. In particular, laser powder bed melting (LPBF) technology, through high-speed localized melting and extreme cooling, achieves high-precision fabrication of micro-pillars, complex nodes, and topology-optimized lattice structures, allowing engineering structures to achieve a new balance between material utilization, mechanical properties, and design freedom. However, the dynamic behavior of the molten pool, thermal cycling characteristics, and rapid solidification microstructure control during LPBF are highly dependent on process parameters, leading to a strong coupling relationship between residual stress, microstructure, and defect formation, which in turn affects the overall performance and manufacturability of lattice components.

[0003] For complex lattice structures, such as T-BCC (Topology-Optimized Body-Centered Cubic), their highly non-uniform geometric support characteristics make them more sensitive to thermal history distribution, grain evolution paths, and local mechanical responses. Existing research typically approaches these issues from single perspectives, such as temperature field simulation, residual stress prediction, grain growth modeling, or mechanical property evaluation, lacking a comprehensive model that can simultaneously characterize the multi-scale correlation between process, microstructure, and performance. Furthermore, in practical applications, lattice structures often require a balance between multiple objectives, including stiffness, energy absorption, and residual stress control. Existing process optimization strategies struggle to effectively address the synergistic control of multiple performance characteristics and lack methods for constructing high-confidence process windows under manufacturability constraints. Summary of the Invention

[0004] This invention aims to construct a collaborative optimization framework that can simultaneously coordinate LPBF process parameters, thermo-mechanical coupling effects, grain structure evolution, and the mechanical properties of T-BCC lattice structures. It describes the multi-scale mapping relationship between process, microstructure, and properties through a multi-output surrogate model, and achieves efficient search and optimal solution extraction of the process parameter space under manufacturability constraints using a multi-objective evolutionary algorithm. This method focuses on accurately predicting residual stress, equivalent stiffness, energy absorption, and grain structure parameters. It replaces the actual forming process with a surrogate model trained by fusing numerical simulation and experimental data, thereby obtaining a high-performance Pareto-dominated process parameter set. Furthermore, it constructs LPBF process windows oriented towards different performance requirements, enabling adaptive, high-quality forming design of T-BCC lattice structures, and providing a systematic process optimization strategy for the engineering application of complex lattice structures.

[0005] 1. A multi-objective collaborative optimization method for laser selective melting (LPBF) process of T-BCC lattice structure is proposed, including the following steps:

[0006] S1. Laser power P, scanning speed v, and powder thickness t constitute the process parameter vector x = [P, v, t]. A multi-output process-microstructure-performance surrogate model f for the T-BCC lattice LPBF forming process is constructed based on random forest regression. RFR (x), the surrogate model output includes the residual stress characterization σ. r Equivalent Young's modulus E*, energy absorption per unit volume SEA, grain size d g The aspect ratio of the grains AR g ;

[0007] S2. Using the output of the surrogate model as a response, construct a multi-objective optimization model with the process parameter vector x as the independent variable: Under the premise of satisfying the energy density and LPBF manufacturability constraints, define a multi-objective performance function vector:

[0008]

[0009] The residual stress σ is achieved by minimizing the objective function vector F(x). r The decrease in the equivalent Young's modulus E* and the simultaneous increase in the energy absorbed per unit volume SEA;

[0010] S3. Select a multi-objective evolutionary algorithm and use the multi-output random forest surrogate model f. RFR (x) Replace the actual forming-testing process and iteratively search the process parameter space to obtain the Pareto non-dominated process parameter set χ for the above multi-objective optimization problem. P ;

[0011] S4. χ P Mapped to the Pvt three-dimensional process space, a high-performance LPBF process window with a T-BCC lattice structure is constructed by clustering or interpolation, and the corresponding recommended range of process parameters is extracted from the process window according to different performance weights.

[0012] 2. According to the present invention, as a further preferred embodiment, the proposed multi-objective performance collaborative optimization method for laser selective melting (LPBF) process for T-BCC lattice structures, wherein the residual stress characterization quantity σ in the training samples of the multi-output process-microstructure-performance proxy model... r The training data was obtained from a thermo-mechanical sequential coupled finite element model established for the T-BCC lattice structure, the finite element model comprising:

[0013] (1) By adopting a layer-by-layer cell activation strategy and a moving Gaussian heat source consistent with the actual scanning path, and explicitly considering interlayer overlap and scanning rotation angle, a function related to time t is obtained: Wherein, ρ(T), c p (T) and k(T) are the temperature-dependent density, specific heat and thermal conductivity of Ti-6Al-4V alloy, respectively;

[0014] (2) The heat source term q(r,t) adopts the same as the actual scanning path s(t) = [x s (t),y s [(t)] Consistent intralayer moving Gaussian surface heat source: Where η is the absorptivity, P is the laser power, and r b Where is the spot radius and h is the thickness of a single layer. To represent the characteristic function of the current forming layer;

[0015] (3) After obtaining the temperature field T(r,t), the structural field displacement u(r,t) and stress σ(r,t) are solved using the thermo-elastic-plastic equilibrium equation:

[0016] σ=C(T):(ε-ε th ), ε th = α(T)(T(r,t)-T0)I, where C(T) is the temperature-dependent elastic stiffness matrix, α(T) is the coefficient of linear expansion, T0 is the substrate preheating temperature, rigid constraints are applied to the substrate side of the nodal surfaces, and convective heat transfer boundary conditions are applied to other surfaces, Ω node Let σ1(r,t) be the volume of the selected node region. end ) represents the principal tensile stress component in this region, σ r This represents the volumetric average value of the principal tensile stress field in this region.

[0017] (4) All forming layers have been scanned and cooled to room temperature T. room Then, the volume Ω of the T-BCC lattice node region is taken. node The principal tensile stress field σ1(r,t) within end The residual stress scalar is defined as: The σ r Used as training labels for the corresponding output components of the random forest regression surrogate model.

[0018] 3. According to the present invention, as a further preferred embodiment, the proposed multi-objective performance collaborative optimization method for laser selective melting (LPBF) process for T-BCC lattice structures, wherein, in the training samples of the multi-output process-microstructure-performance proxy model, the grain size d g AR with grain aspect ratio gThe training data was obtained from a grain evolution phase-field model that considers the coupling effect of crystal orientation and temperature gradient, the phase-field model including:

[0019] (1) Introduce N grain phase field variables φ into the computational domain Ω of the embedded T-BCC unit cell geometry. k (r,t), (k=1,…,N), the total free energy functional is defined as:

[0020]

[0021] in, The direction is the grain boundary normal. The normalized temperature gradient direction is calculated from the aforementioned temperature field, where λ is the penalty coefficient; the interfacial energy coefficient is... Using the β phase <001> Anisotropy forms coupled with orientation and temperature gradient directions: Where e <001> β phase in the construction direction of the component <001> Crystallographic orientation unit vector, ε a ε g These are the anisotropic weighting parameters;

[0022] (2) The time evolution of the phase field of each grain is given by the gradient flow equation: Among them, M k (T) represents the temperature-dependent interface mobility, and μ represents the thermal driving force coefficient. L (θ k ( ) is the crystal orientation angle θ k The relevant local liquidus temperature is used to reflect the preferential growth of grains with different orientations under LPBF cooling conditions;

[0023] (3) When the phase field evolution reaches a steady state, through θ k =0.5 isosurface division to obtain the volume V of each grain g With inertial tensor I g ,by Characterize the equivalent grain size and I g The lengths of the first and second principal axes are denoted as l1 and l2, respectively, and the aspect ratio of the grain is defined as AR. g =l1 / l2, the resulting d g with AR g As training labels for the corresponding output components of the random forest regression surrogate model.

[0024] 4. According to the present invention, as a further preferred embodiment, the proposed multi-objective performance synergistic optimization method for laser selective melting (LPBF) process for T-BCC lattice structures, wherein the thermo-mechanical coupled finite element model and the grain growth phase field model achieve multi-physics coupling through the temperature field, i.e.:

[0025] (1) The spatiotemporal temperature field T(r,t) obtained from the thermo-mechanical finite element analysis is mapped to the computational grid of the phase field model as the external thermal field boundary condition driving the evolution of the phase field;

[0026] (2) Based on the instantaneous cooling rate and temperature gradient in T(r,t), the interface mobility and orientation-related grain boundary energy weights in the phase field model are adaptively adjusted to reflect the changes in grain nucleation density and epitaxial growth rate under different combinations of process parameters.

[0027] (3) The coupling strategy described above guarantees d g AR g With σ r The responses to the same process parameter vector x have a consistent thermal history physical basis.

[0028] 5. According to a further preferred embodiment of the present invention, the proposed multi-objective performance collaborative optimization method for laser selective melting (LPBF) process with T-BCC lattice structure, wherein the training samples of the random forest regression surrogate model are composed of experimentally measured data and numerical simulation data, and multi-source data fusion is performed through sample weights:

[0029] (1) The experimental samples include the equivalent Young's modulus E*, energy absorption SEA, and residual stress measured or pore defect assessment results obtained from the compression test of LPBF-formed T-BCC lattice specimens.

[0030] (2) The simulation samples include d obtained from the thermo-mechanical coupled finite element model and the phase field model. g AR g σ r And E* and SEA obtained from equivalent mechanical simulation;

[0031] (3) During the training of the random forest, the objective function is minimized by the multi-output weighted squared error: Determine the splitting rules and leaf node outputs for each decision tree in the random forest. Where: Q = {σ} r ,d g AR g ,E*,SEA} is a set of multiple output indicators, N exp and N sim These represent the experimental sample size and the simulation sample size, respectively. This is the reference value for the q-th output. The corresponding model prediction value is α>β, which are the weight coefficients of the experimental samples and the simulation samples, and θ is the random forest model parameter, in order to suppress the influence of the numerical model system bias on the surrogate model and achieve collaborative prediction of multiple output performance indicators.

[0032] 6. According to the present invention, as a further preferred embodiment, the proposed multi-objective performance collaborative optimization method for laser selective melting (LPBF) process for T-BCC lattice structures, wherein the LPBF manufacturability constraints in the multi-objective optimization model include at least:

[0033] (1) Linear energy density or volume energy density E calculated from the process parameter vector x = [P, v, t]. d (x) satisfies E d,min ≤E d (x)≤E d,max To avoid incomplete melting and overheating;

[0034] (2) The depth-to-width ratio λ(x) of the molten pool obtained by back-calculation from the thermo-mechanical coupled finite element model is limited to [λ min ,λ max Within the specified range, to ensure stable nucleation of the molten pool and interlayer metallurgical bonding;

[0035] (3) The equivalent density or defect index predicted by the proxy model is not lower than the preset lower limit, thereby ensuring the overall forming quality of the T-BCC lattice.

[0036] 7. According to the present invention, as a further preferred embodiment, the proposed multi-objective performance collaborative optimization method for laser selective melting (LPBF) process oriented towards T-BCC lattice structures, wherein the multi-objective evolutionary algorithm is a multi-objective evolutionary algorithm based on non-dominated sorting, and its iteration process includes:

[0037] (1) Using the process parameter vector x as an individual code, a candidate process parameter population is generated through crossover and mutation;

[0038] (2) Using the random forest proxy model f RFR The output of (x) serves as an estimate of the individual's fitness on various performance targets, replacing actual LPBF forming and experimental testing;

[0039] (3) Using the non-dominated sorting and crowding distance evaluation strategy, uniformly distributed Pareto front individuals are retained until convergence is obtained to obtain the Pareto non-dominated process parameter set χ. P .

[0040] 8. According to a further preferred embodiment of the present invention, the proposed multi-objective performance collaborative optimization method for laser selective melting (LPBF) process for T-BCC lattice structures, wherein the step of constructing a high-performance LPBF process window includes:

[0041] (1) For the Pareto non-dominated process parameter set χ P Clustering or density estimation is performed to divide the similarly distributed combinations of process parameters in the Pvt space into several sub-regions;

[0042] (2) In each subregion, d g AR g σ r Statistical analysis was performed on E* and SEA, and sub-regions were labeled as "residual stress priority", "stiffness priority" or "energy absorption priority" according to performance preferences;

[0043] (3) The parameter ranges of each type of sub-region are used as different recommended regions in the process window to guide the selection of LPBF process for T-BCC lattice under different service conditions.

[0044] In a preferred embodiment of the present invention, Ti-6Al-4V alloy powder is used as raw material to prepare T-BCC lattice structure samples on an LPBF device. The average particle size of the powder is 20-45 μm, the oxygen content is controlled below 0.15%, the forming chamber is protected by high-purity argon gas with an oxygen content controlled below 0.01%, and the substrate preheating temperature is 200°C. The volume fraction of the T-BCC lattice unit cell is controlled at around 15%, and a 10 mm × 10 mm × 10 mm cubic lattice core layer sample is formed by periodic stacking.

[0045] In this embodiment, three process parameters were selected: laser power P = 150–250 W, scanning speed v = 800–1200 mm / s, and powder thickness t = 0.02–0.04 mm. Three levels were selected for each parameter, and a full-factor experiment was used to obtain 27 combinations of process parameters. Compression specimens and tissue / residual stress test specimens were prepared for each parameter combination. The residual stress σ was obtained through XRD residual stress testing, EBSD / SEM tissue observation, and quasi-static compression testing. r Grain size d g Grain aspect ratio AR g Experimental data on equivalent Young's modulus E* and energy absorption per unit volume (SEA) were obtained. The experimental results show that, under unoptimized process conditions, the residual stress ranges from approximately 168 to 282 MPa, the grain size is approximately 15 to 28 μm, the grain aspect ratio is between 2.3 and 8.5, the equivalent Young's modulus is approximately 6.5 to 8.0 GPa, and the SEA is approximately 22 to 30 MJ / m³. The performance exhibits a significant nonlinear variation with process parameters.

[0046] To improve sample coverage, this embodiment further combines thermo-mechanical coupled finite element simulation and phase-field grain evolution simulation to generate several virtual simulation samples within the same process parameter space, bringing the total number of multi-source data sets to approximately 80, including 27 experimental samples and approximately 53 simulation samples. The experimental samples are assigned a weight α = 1, and the simulation samples are assigned a weight β = 0.4. A multi-output random forest regression model is trained using a multi-output weighted squared error objective function J(θ). The random forest contains 300 regression trees, with a maximum depth of 12 and a minimum leaf node sample size of 3. The input is a process parameter vector [P, v, t], and the output includes σ. r d g AR g Five metrics were used: E*, SEA, and E*. The model hyperparameters were optimized through 5-fold cross-validation and grid search. Finally, on the test set, the coefficients of determination R0 for each output metric were determined. 2 Both are greater than 0.93, among which the equivalent Young's modulus E* and the R of SEA are... 2 The residual stress σ reached 0.96 and 0.95 respectively. r R 2 The relative error is approximately 0.94; the absolute values ​​of the relative errors of E* and SEA are mostly controlled within 5%, and the relative errors of the prediction of grain size and grain aspect ratio are controlled within 8%. Compared with the compared linear regression, BP neural network and SVR models, the multi-output random forest model reduces the average RMSE of about 20% to 35% on the five indicators, and the overall prediction accuracy is significantly improved.

[0047] Based on the multi-output surrogate model, this embodiment uses the process parameter vector x = [P, v, t] T As a decision variable, to reduce residual stress σ r Furthermore, by improving E* and SEA as optimization objectives, a multi-objective performance function vector F(x) = [σ] is constructed. r [(x), -E(x), -SEA(x)] T Under the constraints of linear energy density of 0.3–0.6 J / mm² and forming density of not less than 99%, a multi-objective evolutionary algorithm is used to iteratively search within a given process parameter range to obtain the Pareto non-dominated solution set. The Pareto solution is mapped to the Pvt process space, and the solution set is clustered and interpolated to form a continuous high-performance process window band.

[0048] A representative set of optimized process parameters was selected from the Pareto solution set: laser power P = 210 W, scanning speed v = 1000 mm / s, and powder thickness t = 0.03 mm for re-testing and shaping. The re-test results show that under these optimized process conditions, the average residual stress in the T-BCC lattice node region is approximately 195 MPa, a reduction of about 25% compared to a typical unoptimized process (e.g., P = 170 W, v = 800 mm / s, t = 0.04 mm, residual stress approximately 260 MPa); the equivalent Young's modulus increased from approximately 7.1 GPa to approximately 8.3 GPa, an increase of about 17%; and the SEA increased from approximately 24 MJ / m². 3 Increased to approximately 30 MJ / m 3 The efficiency was increased by approximately 25%, while the overall lattice density remained above 99%, with no obvious unmelted defects or severe hot cracks observed. Comparative analysis shows that the optimized process parameters obtained in this embodiment can significantly reduce residual stress while also considering stiffness and energy absorption performance, achieving multi-objective performance synergistic optimization of the T-BCC lattice LPBF process.

[0049] As can be seen from the above preferred embodiments, the multi-source data weighted multi-output random forest surrogate model and its driven multi-objective optimization method proposed in this invention can quantitatively evaluate the residual stress, grain characteristics, and mechanical / energy absorption performance of T-BCC lattice structures with high prediction accuracy, and obtain a high-performance process parameter window with engineering feasibility based on this. Compared with traditional empirical selection or single-objective optimization methods, the embodiments of this invention show significant advantages in residual stress control, stiffness, and energy absorption capacity, thus proving the accuracy and practical value of the method of this invention. Attached Figure Description

[0050] Figures 1(1)-1(3) This is a schematic diagram of the T-BCC lattice structure of the present invention;

[0051] Figure 2 This is a flowchart of the finite element analysis process for the thermo-mechanical coupling model of this invention;

[0052] Figures 3(1)-3(4) This is a simulation diagram of the T-BCC dot matrix forming process of the present invention;

[0053] Figures 4(1)-4(4) This is a simulation result distribution diagram of the residual stress of the T-BCC lattice of the present invention;

[0054] Figure 5 This is a diagram showing the peak residual stress at the T-BCC lattice nodes of different heights according to the present invention.

[0055] Figures 6(1)-6(4) This is a diagram illustrating the influence of the process parameters of this invention on residual stress and equivalent Young's modulus.

[0056] Figure 7 This is a comparison diagram of the simulation and experimental results of the grain structure of the T-BCC lattice node of the present invention;

[0057] Figures 8(1)-8(4) This is a diagram illustrating the influence of laser process parameters on the grain aspect ratio in this invention.

[0058] Figure 9 This is a schematic diagram of the T-BCC lattice structure random forest proxy model of the present invention;

[0059] Figure 10 This is a Spearman correlation coefficient diagram of the input and output parameters of this invention;

[0060] Figures 11(1)-11(2) This is a diagram showing the model prediction results for grain size in this invention;

[0061] Figures 12(1)-12(2) This is a diagram showing the model prediction results for the grain aspect ratio of this invention;

[0062] Figures 13(1)-13(2) The diagram shows the model prediction results of the residual stress of this invention.

[0063] Figures 14(1)-14(2) This is a diagram showing the model prediction results of the equivalent Young's modulus of this invention;

[0064] Figures 15(1)-15(2) This is a diagram showing the model prediction results of the SEA of this invention. Detailed Implementation

[0065] The preferred embodiments of the present invention are described in detail below with reference to the accompanying drawings, but it should be understood that the scope of protection of the present invention is not limited to the specific embodiments.

[0066] Figures 1(1)-1(3) This diagram illustrates the geometric topology of the T-BCC lattice structure unit cell used in this invention, including diagonal braces arranged along the body diagonal and nodes and members periodically arranged along the construction direction. By introducing "T"-shaped spatial support rods into the unit cell, the load-bearing capacity and energy absorption capacity of the lattice structure can be improved while maintaining a relatively low relative density. The diagram shows geometric parameters such as unit cell size, rod diameter, and inclination angle, providing a basic geometric description for subsequently establishing an LPBF forming process-microstructure-property relationship model.

[0067] Figure 2A thermo-mechanical sequential coupled finite element analysis (FEA) process for T-BCC lattice structures is presented. First, a transient thermal analysis model incorporating a moving Gaussian heat source is constructed based on the actual LPBF scanning path to obtain the spatiotemporal temperature field distribution during the forming process. Then, a thermo-elastoplastic constitutive relation is applied to the thermal analysis results to solve for the structural field displacement and stress response, thereby extracting the residual stress characterization parameters of the nodal regions. This flowchart system systematically illustrates key steps such as geometric modeling, mesh generation, process parameter input, boundary condition setting, and result post-processing, providing a computational path for obtaining residual stress training data.

[0068] Figures 3(1)-3(4) This paper presents the layer-by-layer powder laying and scanning simulation process of T-BCC lattice structures in LPBF forming, including the melt pool evolution, interlayer overlap, and the layer-by-layer height increase of the component at typical time steps. By adopting a layer-by-layer element activation strategy and a heat source loading method consistent with the actual scanning trajectory, the figure intuitively reflects the cumulative effect of thermal cycling along the construction direction and the heating characteristics of different layer node regions. This figure provides a visual basis for understanding the thermal history and residual stress formation mechanism of T-BCC lattices in additive manufacturing.

[0069] Figures 4(1)-4(4) The distribution contour plots of the principal tensile stress field of the T-BCC lattice structure after cooling to room temperature under representative process parameter combinations are presented. It can be seen that the residual tensile stress is mainly concentrated in the node intersection region and the bottom layer near the substrate, exhibiting a clear gradient distribution characteristic along the fabrication direction. The results shown in this figure, obtained by taking a volumetric region near the nodes and calculating the average principal tensile stress, are used to define the residual stress scalar σ. r This provides key characterization metrics for subsequent surrogate model output components and multi-objective optimization.

[0070] Figure 5 The figure shows the relationship between the peak value of the principal tensile residual stress at different layer nodes along the construction height direction and the height. The horizontal axis represents the dimensionless construction height or layer number, and the vertical axis represents the peak value of the residual stress in the corresponding node region. It is evident that the residual stress is higher near the substrate and gradually decreases or redistributes with increasing height. This figure reveals the influence of the thermo-mechanical constraint conditions of the LPBF process on the non-uniformity of residual stress in the height direction, providing a basis for selecting representative node regions and formulating residual stress reduction strategies.

[0071] Figures 6(1)-6(4) The effects of process parameters such as laser power P, scanning speed v, and powder thickness t on the residual stress scalar σ are given. r The analysis results regarding the influence of the equivalent Young's modulus E can be presented in the form of response surfaces, contour lines, or parameter-performance curves. The figure shows that, within the range satisfying manufacturability constraints, different combinations of process parameters will lead to σ... rThe process and performance vary synergistically or competitively over a wide range; for example, increasing energy density can improve stiffness but may increase residual stress. This figure quantitatively reveals the multi-objective coupling relationship between process and performance, providing an intuitive reference for constructing process windows and conducting synergistic optimization.

[0072] Figure 7 This paper presents a comparison between phase-field simulation results of the grain structure in the nodal region of the T-BCC lattice and experimentally measured microstructures (such as EBSD or metallography). The figures show that the simulated distribution of columnar and equiaxed crystals, grain orientation, and preferred growth characteristics along the construction direction are in good agreement with experimental observations in terms of morphology and scale. This comparison verifies that the constructed grain evolution phase-field model is effective in characterizing grain size d under LPBF conditions. g AR with aspect ratio g The accuracy of this aspect provides a reliable basis for using its output as training labels for surrogate models.

[0073] Figures 8(1)-8(4) The grain aspect ratio AR is given under different combinations of laser power, scanning speed and powder thickness. g The variation pattern can be represented as a single-factor curve or an isopleth plot in a multi-dimensional parameter space. The figure shows that process parameters, by changing the molten pool shape, cooling rate, and temperature gradient direction, regulate the degree of grain elongation and lateral growth capability in the construction direction, leading to AR... g It exhibits significant process sensitivity. This figure illustrates that by appropriately selecting the process window, the microstructure anisotropy of the T-BCC lattice can be controlled within a certain range, providing a process means for achieving performance-oriented design.

[0074] Figure 9 This is a schematic diagram of the multi-output random forest proxy model structure for T-BCC lattice structures constructed in this invention. The model takes laser power P, scanning speed v, powder thickness t, and energy density derived therefrom as inputs, and outputs the residual stress scalar σ through a random forest regressor composed of multiple decision trees. r Grain size d g Grain aspect ratio AR g The figure also shows various performance indicators such as equivalent Young's modulus E* and energy absorption per unit volume (SEA). The figure also illustrates the multi-source fusion method of experimental data and numerical simulation data, intuitively demonstrating the overall framework of the multi-output proxy modeling of process-microstructure-performance in this invention.

[0075] Figure 10 Spearman correlation coefficient matrix diagrams are presented, showing the relationship between process parameters and derived characteristics and multi-output performance indicators. These diagrams are typically presented as heatmaps or color matrices. This allows for a visual identification of the relationship between each input parameter and σ. r d g ARg The monotonic correlations and their strengths among E* and SEA are illustrated; for example, some parameters show a significant positive correlation with residual stress but a negative correlation with energy absorption capacity. This figure provides a basis for feature selection and interpretive analysis using surrogate models, and helps to understand the potential coupling relationships between multi-objective performance characteristics.

[0076] Figures 11(1)-11(2) This demonstrates the effect of the random forest surrogate model on grain size d. g The prediction results can be presented as a scatter plot comparing predicted and reference values ​​or an error distribution plot. Most sample points in the plot are distributed near the diagonal, indicating that the model has high accuracy and low bias in predicting grain size under different process conditions. Statistical indicators such as the coefficient of determination or mean square error are also provided to quantify the model's performance. This plot verifies the effectiveness of the surrogate model in predicting microstructure size, providing a reliable estimate of the microstructure response for subsequent multi-objective optimization.

[0077] Figures 12(1)-12(2) The surrogate model for grain aspect ratio AR is given. g The figure shows a comparison between the predicted results and phase-field simulation or experimental reference values. As can be seen from the figure, the predicted values ​​are highly consistent with the actual values ​​for most samples, with only minor deviations under extreme process conditions, indicating that the model can effectively capture the influence of process parameters on grain anisotropy evolution. Statistical analysis of the aspect ratio prediction error further demonstrates the reliability of the method of this invention in characterizing microstructure anisotropy.

[0078] Figures 13(1)-13(2) The surrogate model demonstrates the effect of the residual stress scalar σ r The comparison between the predicted values ​​and the finite element simulation results is usually presented as a scatter plot or a fitted curve. In the figure, the sample points are densely distributed along the diagonal, indicating that the model has good consistency and generalization ability in estimating the residual stress level under different combinations of process parameters. This figure shows that the surrogate model can effectively replace the high-cost thermo-mechanical coupled finite element analysis, providing a foundation for the rapid search of multi-objective evolutionary algorithms in the process space.

[0079] Figures 14(1)-14(2) The figure compares the predicted results of the surrogate model for the equivalent Young's modulus E* of the T-BCC lattice with experimental compression tests or mechanical simulation results. As shown in the figure, the deviation between the predicted and reference values ​​is small for most data points, indicating that the model constructed in this invention can accurately reflect the stiffness response of the lattice structure under different process parameters. This figure verifies the rationality of the mapping relationship between process, geometry, and performance, providing support for the synergistic optimization of residual stress and energy absorption performance while meeting stiffness requirements.

[0080] Figures 15(1)-15(2)The surrogate model's predictive ability for energy absorption SEA per unit volume is demonstrated, and the model output is compared with energy absorption indices obtained from experiments or numerical calculations. The figure shows that, under different combinations of process parameters, the predicted values ​​generally agree well with the reference values, effectively distinguishing between process regions with high and low energy absorption. This figure indicates that the multi-output random forest surrogate model of this invention can simultaneously consider multiple performance indices such as stiffness, residual stress, and energy absorption, laying the foundation for constructing high-performance LPBF process windows and obtaining the Pareto optimal process parameter set.

[0081] The overall technical solution of this invention is a multi-objective performance collaborative optimization method for laser selective melting (LPBF) process for T-BCC lattice structures, comprising the following steps:

[0082] S1. Laser power P, scanning speed v, and powder thickness t constitute the process parameter vector x = [P, v, t]. A multi-output process-microstructure-performance surrogate model f for the T-BCC lattice LPBF forming process is constructed based on random forest regression. RFR (x), the surrogate model output includes the residual stress characterization σ. r Equivalent Young's modulus E*, energy absorption per unit volume SEA, grain size d g The aspect ratio of the grains AR g ;

[0083] S2. Using the output of the surrogate model as a response, construct a multi-objective optimization model with the process parameter vector x as the independent variable: Under the premise of satisfying the energy density and LPBF manufacturability constraints, define a multi-objective performance function vector:

[0084]

[0085] The residual stress σ is achieved by minimizing the objective function vector F(x). r The decrease in the equivalent Young's modulus E* and the simultaneous increase in the energy absorbed per unit volume SEA;

[0086] S3. Select a multi-objective evolutionary algorithm and use the multi-output random forest surrogate model f. RFR (x) Replace the actual forming-testing process and iteratively search the process parameter space to obtain the Pareto non-dominated process parameter set χ for the above multi-objective optimization problem. P ;

[0087] S4. χ P Mapped to the Pvt three-dimensional process space, a high-performance LPBF process window with a T-BCC lattice structure is constructed by clustering or interpolation, and the corresponding recommended range of process parameters is extracted from the process window according to different performance weights.

[0088] Example 1: Multi-objective performance co-optimization case study of LPBF process for T-BCC lattice structure

[0089] In this embodiment, Ti-6Al-4V alloy powder was used as raw material to prepare T-BCC lattice structure samples via LPBF process. The proposed "process-microstructure-property" multi-output surrogate model and multi-objective evolutionary optimization method are explained in detail, and combined with... Figures 1(1)-1(3) ~ Figures 15(1)-15(2) The aforementioned formulas provide numerical substitution and experimental comparison results to verify the beneficial effects of the method of the present invention.

[0090] (I) Process parameter range and sample construction (corresponding to S1, Figures 1(1)-1(3) ~ Figures 8(1)-8(4) )

[0091] In this embodiment, the volume fraction of the T-BCC lattice unit cell is controlled at approximately 15%, and a cubic lattice core layer sample with dimensions of approximately 10 mm × 10 mm × 10 mm is formed by periodic stacking. The unit cell geometry is as follows: Figures 1(1)-1(3) As shown.

[0092] Three process parameters were selected: laser power P = 150–250 W, scanning speed v = 800–1200 mm / s, and powder thickness t = 0.02–0.04 mm. Each parameter had three levels, and a full factorial experimental design was used to obtain 27 combinations of process parameters. For each parameter combination, T-BCC lattice specimens were prepared for compression experiments and tissue / residual stress testing. The residual stress σ was obtained through XRD residual stress testing, EBSD / SEM tissue observation, and quasi-static compression testing. r Grain size d g Grain aspect ratio AR g Experimental data included the equivalent Young's modulus E* and the energy absorbed per unit volume (SEA). The results showed that, under unoptimized process conditions, the residual stress was approximately 168–282 MPa, the grain size was approximately 15–28 μm, the grain aspect ratio was between 2.3 and 8.5, the equivalent Young's modulus was approximately 6.5–8.0 GPa, and the SEA was approximately 22–30 MJ / m². 3 .

[0093] To expand the sample coverage, this embodiment further incorporates thermo-mechanical sequential coupling finite element simulation (corresponding to...). Figures 2-5 ) and grain evolution phase-field simulation (corresponding to Figures 7-8(1) -Figure 8(4)) Several virtual simulation samples were generated in the same process parameter space, so that the total number of multi-source data reached about 80 sets, including 27 experimental samples and about 53 simulation samples.

[0094] The thermo-mechanical coupled finite element model employs layer-by-layer element activation and a moving Gaussian heat source, explicitly considering interlayer overlap and scanning rotation angle to obtain the spatiotemporal temperature field of the forming process. The principal tensile stress field in the nodal region is solved using the thermo-elastic-plastic equilibrium equation, and the residual stress scalar σ is defined. r As training labels (corresponding) Figures 2-5 ).

[0095] The grain evolution phase-field model introduces N phase-field variables into the computational domain embedded with T-BCC unit cell geometry. The grain volume V is obtained through a gradient flow equation that couples free energy functionals, interface mobility, and temperature gradient. g With inertial tensor I g Thus, the grain size d can be calculated. g and aspect ratio AR g (correspond Figure 7 , Figures 8(1)-8(4) ).

[0096] The experimental and simulation data mentioned above are used as training samples for the multi-output process-organization-performance proxy model.

[0097] (II) Example of training and formula substitution for a multi-output random forest surrogate model (corresponding to S1) Figures 9 to 15(1) -Figure 15(2))

[0098] According to step S1 of the present invention, the process parameter vector x = [P, v, t] is... T As the model input, the output vector is y = [σ]. r ,E*,SEA,d g AR g ] T Construct a multi-output random forest regression surrogate model, such as Figure 9 As shown.

[0099] During training, experimental samples and numerical simulation samples are fused from multiple sources using a weighted squared error objective function, in the following form:

[0100]

[0101] Where: Q={σ r ,d g AR g E * ,SEA} is a set of multiple output metrics. and These are the reference values ​​for the i-th experimental sample and the j-th simulation sample on the q-th output index, respectively. and The predicted values ​​corresponding to the multi-output random forest surrogate model are denoted by α and β, respectively, representing the weight coefficients of the experimental and simulated samples. θ represents the set of parameters for the random forest model, and J(θ) is the weighted squared error objective function. In this embodiment, N is taken as... exp =27, N sim ≈53. Substituting the specific values ​​into the objective function above: assigning a weight α = 1 to the experimental samples and a weight β = 0.4 to the simulation samples, we obtain the target component loss term for any experimental sample i and the corresponding loss term for the simulation sample j. By substituting all approximately 80 sets of samples into the above weighted error function and minimizing J(θ), we determine the splitting rules and leaf node outputs of each decision tree in the random forest.

[0102] The trained multi-output random forest surrogate model contains approximately 300 regression trees, with a maximum depth of 12 and a minimum leaf node sample size of 3. After optimizing the hyperparameters using 5-fold cross-validation and grid search, the coefficients of determination R0 for each output metric on the test set are... 2 Both are greater than 0.93, among which the equivalent Young's modulus E* and the R of SEA are... 2 The residual stress σ reached approximately 0.96 and 0.95 respectively. r R 2 The relative errors are approximately 0.94; the absolute values ​​of the relative errors of E* and SEA are mostly controlled within 5%, and the relative errors of the grain size and grain aspect ratio predictions are controlled within 8%. Compared with linear regression, BP neural network, and SVR models, the multi-output random forest model of this invention reduces the average RMSE of the five indicators by approximately 20% to 35%, such as... Figures 11(1)-11(2) ~ Figures 15(1)-15(2) As shown.

[0103] (III) Multi-objective optimization model and the substitution calculation of F(x) (corresponding to S2~S3, Figures 6(1)-6(4) , Figure 10 )

[0104] In step S2, the process parameter vector is x = [P, v, t]. T As decision variables, under the premise of satisfying energy density and LPBF manufacturability constraints, construct a multi-objective performance function vector:

[0105]

[0106] Where σ r E*(x), SEA(x) are given by the above multi-output random forest proxy model.

[0107] Manufacturability constraints include at least the following:

[0108] • The linear energy density or volume energy density Ed(x) calculated from the process parameter vector x=[P,v,t]T satisfies 0.3~0.6J / mm to avoid undermelting and overburning;

[0109] • The aspect ratio of the molten pool is within a given range to ensure metallurgical bonding;

[0110] • The equivalent density or defect index predicted by the surrogate model is not less than 99%, thereby ensuring the overall forming quality of the T-BCC lattice.

[0111] Take a set of unoptimized processes as an example:

[0112] Let x0 = [170W, 800mm / s, 0.04mm] T According to the energy density calculation formula in claim 6, substituting P = 170W, v = 800mm / s, and t = 0.04mm yields the linear energy density E. d (x0) is determined to be within the allowable range of 0.3–0.6 J / mm, thus satisfying the manufacturability constraint. Substituting x0 into the random forest surrogate model, we obtain:

[0113] • Residual stress prediction value σ r (x0)≈260MPa,

[0114] The predicted equivalent Young's modulus is E*(x0)≈7.1 GPa.

[0115] • Predicted energy absorption per unit volume SEA(x0)≈24MJ / m 3 .

[0116] The objective function vector for this process point is: F(x0) = [260, -7.1, -24] T

[0117] Similarly, by performing the above F(x) calculation on a large number of candidate points x in the LPBF process parameter search space, and iteratively updating the population using a multi-objective evolutionary algorithm, performing non-dominated sorting and crowding distance filtering, a Pareto non-dominated solution set covering the residual stress-stiffness-energy absorption tradeoff can be obtained, such as... Figures 6(1)-6(4) and Figure 10 What is revealed.

[0118] (iv) Verification of Pareto's preferred process points (corresponding to S3 to S4) Figures 6(1)-6(4) , Figures 11(1)-11(2) ~ Figures 15(1)-15(2) )

[0119] In the Pareto non-dominated solution set mentioned above, this embodiment selects a representative set of preferred process parameters x* = [210W, 1000mm / s, 0.03mm]. TThe point is located Figures 6(1)-6(4) Within the high-performance region characterized by "low residual stress and high stiffness and energy absorption".

[0120] 1. Examples of substituting multi-objective functions F(x)

[0121] Substituting x* into the multi-output random forest surrogate model yields the corresponding predicted values. The deviations between the predicted values ​​and subsequent validation values ​​are mostly controlled within 5%, consistent with the aforementioned surrogate model accuracy evaluation results (see...). Figures 13(1)-13(2) ~ Figures 15(1)-15(2) ).

[0122] In actual testing, T-BCC lattice specimens were formed under the process conditions of P=210W, v=1000mm / s, and t=0.03mm, and residual stress and compression tests were conducted. The measured results were as follows: the average residual stress in the nodal region was approximately 195MPa; the equivalent Young's modulus was approximately 8.3GPa; and the energy absorption per unit volume was approximately 30MJ / m³. 3 The overall density of the lattice remained above 99%, with no obvious unmelted defects or severe hot cracks.

[0123] Therefore, the objective function vector for this preferred process point can be written as: F(x*)≈[195, -8.3, -30] T .

[0124] Compared to the unoptimized process point x0, the improvements in each objective component are as follows: residual stress reduced by 25%; equivalent Young's modulus increased by 17%; and SEA increased by 25%. It can be seen that, under the same relative density and manufacturability constraints, x* simultaneously advances the three objective components in a favorable direction, fully meeting the multi-objective synergistic optimization objective of this invention: "reducing residual stress and simultaneously improving stiffness and energy absorption."

[0125] (v) Beneficial effects shown in this embodiment

[0126] As can be seen from the above specific embodiments:

[0127] σ obtained using thermo-mechanical coupled finite element and grain evolution phase field model r d g AR g The multi-output random forest surrogate model trained with experimental data can simultaneously provide the residual stress, microstructure, and mechanical / energy absorption properties of the T-BCC lattice in a single prediction, with high prediction accuracy and low computational cost.

[0128] Under the manufacturability constraint, with F(x) = [σ r [(x), -E*(x), -SEA(x)] TTo optimize the objective, the Pareto process solution set obtained by using a multi-objective evolutionary algorithm can be used to construct the high-performance LPBF process window shown in the figure, thereby enabling the division and recommendation of process regions with different performance preferences.

[0129] The selected optimal process points P=210W, v=1000mm / s, and t=0.03mm were retested. The residual stress was reduced by about 25%, the equivalent Young's modulus was increased by about 17%, and the SEA was increased by about 25%, while maintaining high density and good forming quality. This fully demonstrates the synergistic optimization effect of the method of the present invention in terms of residual stress control, stiffness improvement and energy absorption enhancement.

[0130] The above preferred embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it. They should not be used to limit the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the essence of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A multi-objective collaborative optimization method for laser powder bed melting process of topology-optimized body-centered cubic lattice structures, characterized in that, Includes the following steps: S1. Laser power P, scanning speed v, and powder thickness t constitute the process parameter vector x = [P, v, t]. A multi-output process-microstructure-performance surrogate model f for the T-BCC lattice LPBF forming process is constructed based on random forest regression. RFR (x), the surrogate model output includes the residual stress characterization σ. r Equivalent Young's modulus E*, energy absorption per unit volume SEA, grain size d g The aspect ratio of the grains AR g ; S2. Using the output of the surrogate model as a response, construct a multi-objective optimization model with the process parameter vector x as the independent variable: Under the premise of satisfying the energy density and LPBF manufacturability constraints, define a multi-objective performance function vector: The residual stress σ is achieved by minimizing the objective function vector F(x). r The decrease in the equivalent Young's modulus E* and the simultaneous increase in the energy absorbed per unit volume SEA; S3. Select a multi-objective evolutionary algorithm and use the multi-output random forest surrogate model f. RFR (x) Replace the actual forming-testing process and iteratively search the process parameter space to obtain the Pareto non-dominated process parameter set χ for the above multi-objective optimization problem. P ; S4. χ P Mapped to the Pvt three-dimensional process space, a high-performance LPBF process window with a T-BCC lattice structure is constructed by clustering or interpolation, and the corresponding recommended range of process parameters is extracted from the process window according to different performance weights.

2. The method according to claim 1, characterized in that, In the training samples of the multi-output process-microstructure-performance proxy model, the residual stress characterization quantity σ r The training data was obtained from a thermo-mechanical sequential coupled finite element model established for the T-BCC lattice structure, the finite element model comprising: (1) Using a layer-by-layer unit activation strategy and a moving Gaussian heat source consistent with the actual scanning path, and explicitly considering interlayer overlap and scanning rotation angle, a function related to time t is obtained: Wherein, ρ(T), c p (T) and k(T) are the temperature-dependent density, specific heat and thermal conductivity of Ti-6Al-4V alloy, respectively; (2) The heat source term q(r,t) adopts the same as the actual scanning path s(t) = [x s (t),y s [(t)] Consistent intralayer moving Gaussian surface heat source: Where η is the absorptivity, P is the laser power, and r b Where is the spot radius and h is the thickness of a single layer. To represent the characteristic function of the current forming layer; (3) After obtaining the temperature field T(r,t), the structural field displacement u(r,t) and stress σ(r,t) are solved using the thermo-elastic-plastic equilibrium equation: σ=C(T):(ε-ε th ), ε th = α(T)(T(r,t)-T0)I, where C(T) is the temperature-dependent elastic stiffness matrix, α(T) is the coefficient of linear expansion, T0 is the substrate preheating temperature, rigid constraints are applied to the substrate side of the nodal surfaces, and convective heat transfer boundary conditions are applied to other surfaces, Ω node Let σ1(r,t) be the volume of the selected node region. end ) represents the principal tensile stress component in this region, σ r This represents the volumetric average value of the principal tensile stress field in this region; (4) All forming layers have been scanned and cooled to room temperature T. room Then, the volume Ω of the T-BCC lattice node region is taken. node The principal tensile stress field σ1(r,t) within end The residual stress scalar is defined as: The σ r Used as training labels for the corresponding output components of the random forest regression surrogate model.

3. The method according to claim 1 or 2, characterized in that, In the training samples of the multi-output process-structure-performance proxy model, the grain size d g AR of grain length and width g The training data was obtained from a grain evolution phase-field model that considers the coupling effect of crystal orientation and temperature gradient, the phase-field model including: (1) Introduce N grain phase field variables φ into the computational domain Ω of the embedded T-BCC unit cell geometry. k (r,t), (k=1,…,N), the total free energy functional is defined as: in, The direction is the normal direction of the grain boundary. The normalized temperature gradient direction is calculated from the temperature field obtained in claim 2, where λ is the penalty coefficient; the interface energy coefficient is... Using the β phase <001> Anisotropy forms coupled with orientation and temperature gradient directions: Where e <001> β phase in the construction direction of the component <001> Crystallographic orientation unit vector, ε a ε g These are the anisotropic weighting parameters; (2) The time evolution of the phase field of each grain is given by the gradient flow equation: Among them, M k (T) represents the temperature-dependent interface mobility, and μ represents the thermal driving force coefficient. L (θ k ( ) is the crystal orientation angle θ k The relevant local liquidus temperature is used to reflect the preferential growth of grains with different orientations under LPBF cooling conditions; (3) When the phase field evolution reaches a steady state, through θ k =0.5 isosurface division to obtain the volume V of each grain g With inertial tensor I g ,by Characterize the equivalent grain size and I g The lengths of the first and second principal axes are denoted as l1 and l2, respectively, and the aspect ratio of the grain is defined as AR. g =l1 / l2, the resulting d g with AR g As training labels for the corresponding output components of the random forest regression surrogate model.

4. The method according to claim 3, characterized in that, The thermo-mechanical coupled finite element model and the grain growth phase field model are coupled through a temperature field to achieve multi-physics coupling, i.e.: (1) The spatiotemporal temperature field T(r,t) obtained from the thermo-mechanical finite element analysis is mapped to the computational grid of the phase field model as the external thermal field boundary condition driving the evolution of the phase field; (2) Based on the instantaneous cooling rate and temperature gradient in T(r,t), the interface mobility and orientation-related grain boundary energy weights in the phase field model are adaptively adjusted to reflect the changes in grain nucleation density and epitaxial growth rate under different combinations of process parameters. (3) The coupling strategy described above guarantees d g AR g With σ r The responses to the same process parameter vector x have a consistent thermal history physical basis.

5. The method according to claim 4, characterized in that, The training samples of the random forest regression surrogate model are composed of experimentally measured data and numerical simulation data, and multi-source data are fused through sample weights: (1) The experimental samples include the equivalent Young's modulus E*, energy absorption SEA, and residual stress measured or pore defect assessment results obtained from the compression test of LPBF-formed T-BCC lattice specimens. (2) The simulation samples include d obtained from the thermo-mechanical coupled finite element model and the phase field model. g AR g σ r And E* and SEA obtained from equivalent mechanical simulation; (3) During the training of the random forest, the objective function is minimized by the multi-output weighted squared error: Determine the splitting rules and leaf node outputs for each decision tree in the random forest. Where: Q = {σ} r ,d g AR g E * ,SEA} is a set of multiple output metrics, N exp and N sim These represent the experimental sample size and the simulation sample size, respectively. q (i) and y q (j) These are the reference values ​​for the i-th experimental sample and the j-th simulation sample on the q-th output index, respectively. and θ represents the predicted value corresponding to the multi-output random forest surrogate model; α and β are the weight coefficients of the experimental sample and the simulation sample, respectively; θ is the set of parameters of the random forest model, and J(θ) is the weighted squared error objective function.

6. The method according to claim 5, characterized in that, The LPBF manufacturability constraints in the multi-objective optimization model include at least the following: (1) Linear energy density or volume energy density E calculated from the process parameter vector x = [P, v, t]. d (x) satisfies E d,min ≤E d (x)≤E d,max To avoid incomplete melting and overheating; (2) The depth-to-width ratio λ(x) of the molten pool obtained by back-calculation from the thermo-mechanical coupled finite element model is limited to [λ]. min ,λ max Within the specified range, to ensure stable nucleation of the molten pool and interlayer metallurgical bonding; (3) The equivalent density or defect index predicted by the proxy model is not lower than the preset lower limit, thereby ensuring the overall forming quality of the T-BCC lattice.

7. The method according to claim 6, characterized in that, The multi-objective evolutionary algorithm is a non-dominated sorting-based multi-objective evolutionary algorithm, and its iteration process is as follows: (1) Using the process parameter vector x as an individual code, a candidate process parameter population is generated through crossover and mutation; (2) Using the random forest proxy model f RFR The output of (x) serves as an estimate of the individual's fitness on various performance targets, replacing actual LPBF forming and experimental testing; (3) Using the non-dominated sorting and crowding distance evaluation strategy, uniformly distributed Pareto front individuals are retained until convergence is obtained to obtain the Pareto non-dominated process parameter set χ. P .

8. The method according to claim 7, characterized in that, The steps for constructing the high-performance LPBF process window include: (1) For the Pareto non-dominated process parameter set χ p Clustering or density estimation is performed to divide the similarly distributed combinations of process parameters in the Pvt space into several sub-regions; (2) In each subregion, d g AR g σ r Statistical analysis was performed on E* and SEA, and sub-regions were labeled as "residual stress priority", "stiffness priority" or "energy absorption priority" according to performance preferences; (3) The parameter ranges of each type of sub-region are used as different recommended regions in the process window to guide the selection of LPBF process for T-BCC lattice under different service conditions.

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