Multi-objective optimization method for optimizing LPBF parameters based on NSGA-II algorithm
Patent Information
- Application Number
- CN202511298553.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-11
- Publication Date
- 2026-01-23
Smart Images
Figure CN121389417A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of metal powder additive manufacturing, and particularly relates to a multi-objective optimization method for parameter optimization of LPBF based on an NSGA-II algorithm. BACKGROUND
[0002] As an advanced additive manufacturing technology, Laser Powder Bed Fusion (LPBF) has a broad application prospect in strategic emerging industries such as aerospace, national defense and military industry, biomedicine and marine equipment due to its high forming precision and rapid manufacturing, and has attracted widespread attention. However, during the LPBF forming process, due to the extremely fast heating and cooling of the powder and its severe temperature gradient, uneven expansion and shrinkage often occur inside the workpiece, which leads to high residual stress, large deformation, easy-to-initiate cracks, pores and even cracking of the workpiece. Relying solely on post-processing methods cannot completely solve these problems, therefore, optimizing the forming process parameters is particularly important for controlling residual stress and deformation, preventing cracking and other objectives.
[0003] In recent years, machine learning technology has been widely used in modeling and parameter optimization of the relationship between forming parameters and performance indicators. Compared with the traditional trial-and-error method, such data-driven modeling method greatly improves the research efficiency and reduces the experimental cost. However, current related researches are mostly limited to single-objective optimization, and fail to fully consider the coupling relationship between multiple forming parameters and the collaborative optimization problem of multiple performance indicators such as deformation, residual stress and density, thus it is difficult to achieve systematic control of the comprehensive performance of the workpiece. In addition, there is insufficient research on multi-objective parameter combination optimization for LPBF process.
[0004] In summary, the existing optimization methods cannot meet the multi-objective and high-performance forming requirements of the LPBF process. SUMMARY
[0005] The main purpose of the application is to provide a multi-objective optimization method for parameter optimization of LPBF based on an NSGA-II algorithm. The multi-objective collaborative optimization method provided by the application obtains an accurate relationship model between forming parameters and target performance through machine learning for calculation, finds a more optimal forming parameter combination, and thus obtains a workpiece with more excellent performance, which can take into account multiple forming performances and systematically optimize the process parameter combination, providing a theoretical basis and technical support for the manufacturing of high-performance workpieces of LPBF.
[0006] The application provides a multi-objective optimization method for parameter optimization of LPBF based on an NSGA-II algorithm, which comprises the following steps:
[0007] S1, establish a data set and divide the data set into a training set and a test set; wherein the training set and the test set each independently contain forming parameters and part performance, and the part performance includes multiple target performances;
[0008] S2, use the training set to construct multiple prediction models corresponding to each target performance;
[0009] S3, use the test set to evaluate the multiple prediction models to obtain the best prediction model corresponding to each target performance;
[0010] S4, optimize the best prediction model of multiple target performances by using a second-generation non-dominated sorting genetic algorithm to generate a first Pareto front and obtain a multi-objective optimization result; the multi-objective optimization result includes multiple data groups, and each data group independently contains forming parameters and multiple target performances;
[0011] S5, active iterative optimization: perform experiments on the optimal n data groups in the multi-objective optimization result and feed back the experimental results to the data set to perform multiple active iterative optimizations to obtain an optimal solution.
[0012] In some embodiments of the present application, in step S1, the establishment of the data set includes:
[0013] S1-1, data collection: screen forming parameters that affect target performance, use Pearson correlation coefficient as a correlation analysis index to verify the correlation of the forming parameters, and then collect data of the relevant forming parameters and target performance;
[0014] S1-2, data preprocessing: clean the data, perform min-max standardization on the data, and divide the data into the training set and the test set in a ratio of 8:2.
[0015] In some embodiments of the present application, in step 1-1, the method for verifying correlation by using Pearson correlation coefficient includes:
[0016] The calculation formula of Pearson correlation coefficient is represented as:
[0017]
[0018] In the formula, x i and y i represent the values of two variables in the i-th sample in the data set, and x a and y a are the average values of the two variables x and y in all samples in the data set.
[0019] In some embodiments of the present application, the correlation verification is performed by using the Pearson correlation coefficient |r|, where |r| = -1 indicates that the two variables x and y are in a complete negative correlation, |r| = 0 indicates that the two variables x and y are not in a significant linear correlation, and |r| = 1 indicates that the two variables x and y are in a complete positive correlation. When |r| is less than or equal to 0.95, it indicates that the two forming parameters are not strongly correlated, and the corresponding forming parameters are retained. When |r| is greater than 0.95, it indicates that the two forming parameters are strongly correlated, and the forming parameter with the optimal prediction accuracy is retained, and the other is excluded.
[0020] In some embodiments of the present application, in step 1-2, all the data obtained after cleaning are subjected to min-max standardization.
[0021]
[0022] In the formula, x norm is the standardized value, x i is the original data of a certain feature, x max and x min are the maximum and minimum values of the original data of the feature, respectively.
[0023] In some embodiments of the present application, in step S2, the construction method of the plurality of prediction models comprises:
[0024] S2-1, using seven regression algorithms in machine learning, i.e., SVR, RF, DT, GBDT, XGBoost, LGBM, and MLP, and the python language to train the training set to obtain seven initial models;
[0025] S2-2, using Bayesian optimization and 5-fold cross-validation to optimize the hyperparameters of the seven initial models to obtain seven prediction models.
[0026] In some embodiments of the present application, in step S3, the evaluation method of the plurality of prediction models comprises:
[0027] The forming parameters in the test set are input into the plurality of prediction models to obtain a plurality of model prediction performance values, and the average absolute error, the square root error, and the determination coefficient of each model prediction performance value and the corresponding target performance value are calculated to evaluate the plurality of prediction models, and the model with the smallest average absolute error and / or square root error and the determination coefficient closest to 1 is selected as the optimal prediction model.
[0028] In some embodiments of the present application, in step S4, the process of optimizing the optimal prediction models of the plurality of target performances by using the second-generation non-dominated sorting genetic algorithm comprises:
[0029] S4-1, set the objective function, related parameters and the search space of corresponding shaping parameters, wherein the related parameters include population size, iteration number N, crossover probability and mutation probability;
[0030] S4-2, perform the calculation of the second-generation non-dominated sorting genetic algorithm.
[0031] In some embodiments of the present application, the iteration number N is 100.
[0032] In some embodiments of the present application, in step S4-2, the calculation step of the second-generation non-dominated sorting genetic algorithm comprises:
[0033] S4-2-1, complete fast non-dominated sorting by screening non-dominated individuals layer by layer and assigning increasing non-dominated levels until the entire population is layered;
[0034] S4-2-2, calculate the crowding degree of individuals, preferentially select individuals with higher crowding degree, and make the population diversified and promote the uniform distribution of individuals in the same non-dominated level in the target space, the crowding degree calculation formula is:
[0035]
[0036] In the formula, L[i] d represents the crowding distance of individual i; L[i+1] m represents the function value of the mth objective of the ith+1 individual; and are the maximum and minimum values of the mth objective function in the set;
[0037] S4-2-3, select excellent individuals in the population by using non-dominated sorting and the calculated crowding degree, generate a new population by crossover and mutation, and merge the population;
[0038] S4-2-4, repeat the steps of S4-2-1 to S4-2-3 for N times, complete N times of iteration calculation, generate a Pareto front, and generate a multi-objective optimization result.
[0039] In some embodiments of the present application, in step S5, the steps of active iteration optimization are as follows:
[0040] S5-1, normalize all target performances in the multi-group target optimization results to eliminate data scale differences, and calculate the evaluation function Z according to the normalized values, the calculation formula is:
[0041]
[0042] In the formula, POR * , RS * , and DFM *Z value represents the comprehensive performance of the multi-objective optimization result in the solution set;
[0043] S5-2, sort the multiple data groups in the multiple sets of target optimization results, select the data group with the lowest function value, obtain the forming parameter combination of the data group; based on the forming parameter combination, perform actual LPBF titanium part forming, test the porosity, residual stress and deformation amount of the part, add the values to the training set again, train the best prediction model again, and then repeat step S4 to perform the next multi-objective optimization;
[0044] S5-3, the optimized result is the result of one active iteration, and steps S5-1 and S5-2 are repeated for multiple active iterations;
[0045] S5-4, calculate the average Z value of the multiple data groups obtained in each iteration When the improvement rate of the Z value is less than 5%, the iteration is stopped;
[0046] S5-5, in the Pareto frontier of the last active iteration, select the data group with the lowest Z value as the optimal solution.
[0047] In some embodiments of the present application, the forming parameters include process parameters, scanning strategies and support structures; wherein the process parameters include laser power, scanning speed and scanning pitch; the scanning strategy includes scanning line length, interlayer rotation angle and support tooth height; the support structure includes support tooth top width and support tooth root width; and the part performance includes three target performances, namely porosity, residual stress and deformation amount.
[0048] The present application aims at the problem that the coupling optimization effect of the forming parameters and the multi-objective collaborative optimization of the target parameters are not considered in the machine learning in the LPBF control deformation cracking research, and further optimization is performed based on the machine learning result. The algorithm of NSGA-II is introduced after machine learning, and multiple iteration optimizations are performed through active learning to obtain a forming parameter combination with better performance.
[0049] The method provided by the present application realizes multi-objective collaborative optimization, is simple and easy to apply, has accurate optimization results, and has high use value.
[0050] The above description is only a summary of the technical solutions of the present application. In order to more clearly understand the technical means of the present application, the content of the specification can be implemented, and in order to make the above and other purposes, characteristics and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application are described below. BRIEF DESCRIPTION OF DRAWINGS
[0051] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. In the drawings:
[0052] Figure 1 This is a flowchart of a multi-objective optimization method for LPBF parameter optimization based on the NSGA-II algorithm in some embodiments of the present invention.
[0053] Figure 2 The diagram shows the PCC correlation calculation results in some embodiments of the present invention.
[0054] Figure 3 The image shows an LPBF formed part used in experiments measuring residual stress, deformation, and porosity in some embodiments of the present invention.
[0055] Figure 4 This is a Pareto front result diagram generated through multiple active iterations in some embodiments of the present invention; wherein, Figure 4 (a) to (d) in the figure represent the Pareto results generated by the first to the fourth active iterations, respectively.
[0056] Figure 5 This is a comparison chart of the tensile strength and elongation of the multi-objective optimized part and the actual part in some embodiments of the present invention.
[0057] Figure 6 This is a comparison diagram of the impact toughness and fracture toughness of the multi-objective optimized part and the actual part in some embodiments of the present invention. Detailed Implementation
[0058] Exemplary embodiments of the present invention will now be described in more detail with reference to specific examples. It should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this invention will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
[0059] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention; the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and foregoing description of the invention, are intended to cover non-exclusive inclusion.
[0060] In the description of the embodiments of the present invention, the technical terms "first" and "second" are used only to distinguish different objects and should not be construed as indicating or implying relative importance or implicitly indicating the number, specific order or primary and secondary relationship of the indicated technical features.
[0061] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.
[0062] In the description of the embodiments of this invention, the term "and / or" is merely a description of the association relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A exists, A and B exist simultaneously, and B exists. Additionally, the character " / " in this document generally indicates that the preceding and following related objects have an "or" relationship.
[0063] In the description of the embodiments of the present invention, the term "multiple" refers to two or more (including two), similarly, "multiple sets" refers to two or more (including two sets), and "multiple pieces" refers to two or more (including two pieces).
[0064] The multi-objective optimization method for LPBF parameter optimization based on the NSGA-II algorithm provided in this invention is carried out according to the following steps.
[0065] S1. Establish a dataset and divide it into a training set and a test set. The training set and the test set each contain forming parameters and part performance independently. The part performance includes multiple target performance parameters.
[0066] In some embodiments, forming parameters are used as input parameters, including process parameters, scanning strategy, and support structure; wherein, process parameters include laser power, scanning speed, and scanning spacing; scanning strategy includes scanning line length, interlayer rotation angle, and support tooth height; support structure includes support tooth top width and support tooth root width.
[0067] In some embodiments, part performance is used as an output parameter, and part performance includes three target properties: porosity, residual stress, and deformation.
[0068] In some embodiments, the effects of forming parameters on three target properties—porosity, residual stress, and deformation—are mainly studied. There are eight forming parameters: laser power (P), scanning speed (V), hatch spacing (H), scanline length (SL), inter-layer rotation angle (IRA), total height (TH), total top width (TTW), and total root width (TRW).
[0069] In some embodiments, the creation of the dataset specifically includes:
[0070] S1-1, Data Acquisition: Collect relevant data from literature reports and actual experiments, screen out forming parameters that affect the target performance, use Pearson Correlation Coefficient (PCC) as a correlation analysis index to verify the correlation of forming parameters, and remove or retain data of forming parameters. For example, PCC can be used to remove the forming parameter with lower prediction accuracy among two strongly correlated forming parameters.
[0071] In some embodiments, the formula for calculating the Pearson correlation coefficient is expressed as:
[0072]
[0073] In the formula, x i and y i Let x represent the values of the two variables in the i-th sample of the dataset. a and y a This represents the average of two variables, x and y, across all samples in the dataset.
[0074] In some embodiments, when using the Pearson correlation coefficient |r| as a correlation analysis index to verify the correlation of forming parameters, |r| = -1 indicates that the two variables x and y are completely negatively correlated; or, when |r| = 0, it indicates that the two variables x and y are not significantly linearly correlated; or, when |r| = 1, it indicates that the two variables x and y are completely positively correlated. Generally, when |r| exceeds 0.95, it is determined that the two forming parameters are strongly correlated, and the forming parameter with the best prediction accuracy is retained, while the other is discarded. When |r| is less than or equal to 0.95, it is determined that the two forming parameters are not strongly correlated, and both forming parameters are retained. For example, when Figure 2When the absolute value |r| within the grid shown is greater than 0.95, it indicates a strong correlation, and the forming parameter with the best prediction accuracy is retained; when Figure 2 When the absolute value of the value |r| in the grid shown is less than or equal to 0.95, it indicates a weak correlation, and the selected forming parameter will not be eliminated.
[0075] S1-2, Data Preprocessing: Clean the data, remove duplicate and outlier values, focus on removing data with missing key fields, perform min-max standardization on the data, and divide the data into training and test sets in an 8:2 ratio.
[0076] In some embodiments, all data obtained after cleaning are standardized by performing the following calculations:
[0077]
[0078] In the formula, x norm x is the standardized value. i For the original data of a certain feature, x max and x min These represent the maximum and minimum values of the original feature data, respectively.
[0079] S2 uses the training set to construct multiple prediction models corresponding to the performance of each target.
[0080] In some embodiments, the method for constructing multiple prediction models corresponding to each target performance specifically includes:
[0081] S2-1 uses seven regression algorithms in machine learning, namely SVR, RF, DT, GBDT, XGBoost, LGBM, and MLP, and the Python language to train the training set to obtain seven initial models.
[0082] S2-2, using Bayesian optimization and 5-fold cross-validation, the hyperparameters of the above 7 initial models were optimized to obtain 7 prediction models.
[0083] S3. The test set is used to evaluate the above prediction models to obtain the best prediction model for each target performance.
[0084] In some embodiments, the evaluation method for the multiple prediction models includes: inputting the shaping parameters in the test set into multiple prediction models to obtain multiple model prediction performance values, and evaluating the multiple prediction models by calculating the mean absolute error, square root error and coefficient of determination of each model prediction performance value and the corresponding target performance value.
[0085] Specifically, the three evaluation parameters of all prediction models corresponding to each target performance are calculated, and the model with the smallest mean absolute error and / or square root error and the coefficient of determination closest to 1 is selected as the best prediction model.
[0086] For example, multiple prediction models corresponding to residual stress are constructed using a training set, and then the multiple prediction models are evaluated using a test set. Specifically, the forming parameters in the test set are input into the multiple prediction models to obtain multiple model prediction performance values, i.e. multiple residual stress prediction values. The multiple prediction models are evaluated by calculating the mean absolute error, square root error, and coefficient of determination of each residual stress prediction value and the target residual stress value, and the best prediction model for the corresponding residual stress is obtained.
[0087] It should be noted that the target performance value corresponds to the input forming parameters. For example, the target residual stress value corresponds to the input forming parameters.
[0088] In some embodiments, mean absolute error (MAE) is a robustness indicator for measuring model prediction error in regression analysis. It directly reflects the physical magnitude of the prediction bias by calculating the mean of the absolute differences between the predicted and actual values. The formula is as follows:
[0089]
[0090] In the formula, y represents the predicted values corresponding to the three objectives. i This represents the original data, or true values, of the three targets in the dataset.
[0091] In some embodiments, the square root error is an error index that quantifies the overall magnitude of the model's prediction deviation by calculating the square root of the mean of the squared errors between the predicted and actual values. Its formula is as follows:
[0092]
[0093] In the formula, y represents the predicted values corresponding to the three objectives. i This represents the original data, or true values, of the three targets in the dataset.
[0094] In some embodiments, the coefficient of determination is a core indicator for evaluating the explanatory power of a regression model. The closer it is to 1, the stronger the explanatory power of the independent variable on the dependent variable, and the higher the model fit. Its formula is:
[0095]
[0096] In the formula, y represents the predicted values corresponding to the three objectives. i This represents the original data, or true values, of the three objectives in the dataset. This represents the average of the three objectives.
[0097] S4 optimizes the best prediction model for multiple objective performances using the second-generation non-dominated sorting genetic algorithm (NSGA-II), generates the Pareto front, and obtains the calculation results of multi-objective optimization, i.e., the multi-objective optimization results.
[0098] In some embodiments, the process of optimizing the best prediction model for multiple target performances using NSGA-II includes:
[0099] S4-1 sets the search space for the objective function, relevant parameters, and corresponding shaping parameters. The relevant parameters include the population size, number of iterations N, crossover probability, and mutation probability.
[0100] In some embodiments, the population size is set to 200, the number of iterations N is 100, the crossover probability is 0.9, and the mutation probability is 0.08.
[0101] In some embodiments, the objective function is as follows:
[0102] minf(x)=min{y1(x), y2(x), y3(x)}.
[0103] In the formula: y1(x), y2(x) and y3(x) represent the fitness functions of porosity, residual stress and deformation, respectively, which are the optimal prediction models established in step S3 above.
[0104] In some embodiments, the molding parameter search space is set as shown in Table 1.
[0105] Table 1
[0106] Shaping parameter Unit Spatial range Laser power W 80～400 Scan speed mm / s 200～2000 Scan pitch mm 0.04～0.2 Scan line length mm 1～5 Interlayer rotation angle ° 0～90 Support tooth height mm 0～2.4 Support tooth top width mm 0～1.8 Support tooth root width mm 0～2
[0107] S4-2, perform the NSGA-II algorithm calculation.
[0108] S4-2-1 involves rapidly sorting non-dominated individuals by progressively selecting non-dominated individuals and assigning them increasing levels of non-dominance until the entire population is stratified.
[0109] S4-2-2, Calculate individual crowding degree, prioritize individuals with higher crowding degree to diversify the population and promote the even distribution of individuals of the same non-dominant level in the target space. The crowding degree calculation formula is:
[0110]
[0111] In the formula: L[i] dL[i+1] represents the crowding distance of individual i. m Let m be the function value representing the m-th objective of the (i+1)-th individual; and It represents the maximum and minimum values of the m-th objective function in the set.
[0112] S4-2-3 uses non-dominated sorting and calculated crowding to select superior individuals from the population, generates a new population through crossover and mutation, and merges the populations.
[0113] S4-2-4, repeat steps S4-2-1 to S4-2-3 N times, that is, complete N iterations of calculation, generate multi-objective optimization results, that is, generate a Pareto front.
[0114] In some embodiments, the multi-objective optimization results include multiple sets of data, each set independently containing forming parameters and multiple target performance parameters. For example, each set of data independently includes porosity, residual stress, deformation, and laser power (P), scanning speed (V), hatch spacing (H), scanline length (SL), inter-layer rotation angle (IRA), total height (TH), total top width (TTW), and total root width (TRW).
[0115] It is worth mentioning that the solution set of the generated Pareto front contains multiple optimization results. It can be understood that each optimization result corresponds to a set of data, that is, one optimization result corresponds to a set of shaping parameters and multiple target performances.
[0116] In some embodiments, the number of iterations N is set such that the target performance decreases and tends to stabilize after N iterations; for example, the number of iterations N can be set to 100.
[0117] S5, Active Iterative Optimization: Experiment with the best n sets of data from the multi-objective optimization results, feed the experimental results back to the dataset, perform multiple active iterative optimizations, sort the results of the last iteration optimization by Z value, and obtain the optimal solution.
[0118] In some embodiments, the steps for actively iterating to obtain the optimal solution are as follows:
[0119] S5-1, normalize all objective performances (or all objective performances in multiple sets of objective optimization results) within the solution set of the Pareto front obtained in step S4-2-4 to eliminate data scale differences. Calculate the evaluation function Z based on the normalized values. The calculation formula is as follows:
[0120]
[0121] In the formula: POR * RS * DFM * These are the normalized mapping values of the three objective performance values—porosity, residual stress, and deformation—in the Pareto front. The Z value represents the comprehensive performance of the multi-objective optimization results in the solution set; the lower the Z value, the better the comprehensive performance of the results.
[0122] S5-2 sorts all results in the solution set of the Pareto front and selects the results with lower Z values to obtain the optimal n sets of data.
[0123] Actual LPBF titanium parts are formed based on the forming parameters in each result or data set, and the porosity, residual stress, and deformation of each titanium part are tested.
[0124] The actual data values for each titanium component are added back to the dataset, the best prediction model is trained again, and then step S4 is repeated for the next multi-objective optimization.
[0125] S5-3: Take the multi-objective optimization result generated in step S4 as the result of one active iteration, and repeat steps S5-1 and S5-2 for multiple active iterations.
[0126] S5-4, Calculate the average Z-value of the multi-objective optimization results obtained in each iteration. The improvement rate, when When the improvement rate is significantly lower than 5%, it is considered to have achieved the best overall performance, and the iteration is stopped.
[0127] S5-5: In the Pareto front of the last active iteration, the multi-objective optimization result with the lowest Z value is selected as the optimal solution.
[0128] Unless otherwise defined, the technical terms used in the following embodiments have the same meaning as commonly understood by those skilled in the art. Unless otherwise specified, the experimental reagents used in the following embodiments are all conventional biochemical reagents; the raw materials, instruments, and equipment used in the following embodiments can all be obtained commercially or through existing methods; unless otherwise specified, the amounts of experimental reagents used are the amounts used in conventional experimental operations; unless otherwise specified, the experimental methods are conventional methods. It should be further noted that the following description is merely exemplary and not a specific limitation of the present invention.
[0129] Example 1
[0130] The optimal process parameters and part properties, including residual stress, deformation, and porosity, of LPBF-formed TA15 titanium alloy parts were optimized through multi-objective optimization.
[0131] S1. Dataset Establishment: Relevant data were collected from literature reports and actual experiments. Forming parameters affecting residual stress, deformation, and porosity were identified, namely laser power, scanning speed, scanning spacing, scanning line length, interlayer rotation angle, support tooth height, support tooth tip width, and support tooth root width. The Pearson correlation coefficient was used as a correlation analysis index to verify the correlation of the forming parameters. The calculation results are as follows: Figure 2 As shown, there is no strong correlation between the forming parameter and the target performance, so there is no need to exclude them. Data on the forming parameter and the target performance are then collected. The collected data is cleaned to remove duplicates and outliers, with a focus on removing data with missing key fields. The data is then standardized using the min-max method, and finally divided into training and testing sets in an 8:2 ratio.
[0132] S2 uses seven regression algorithms from machine learning—SVR, RF, DT, GBDT, XGBoost, LGBM, and MLP—to train the training set for residual stress, deformation, and porosity, respectively, using Python. This yields seven initial models for residual stress, deformation, and porosity. Then, Bayesian optimization and 5-fold cross-validation are used to optimize the hyperparameters of these seven initial models, resulting in seven predictive models for residual stress, deformation, and porosity.
[0133] S3. The above 7 prediction models are evaluated using the test set to obtain the best prediction model for residual stress, the best prediction model for deformation, and the best prediction model for porosity.
[0134] S4. The three best prediction models mentioned above are optimized using the NSGA-II algorithm to generate the Pareto front, yielding the multi-objective optimization results. The population size is set to 200, the number of iterations N to 100, the crossover probability to 0.9, and the mutation probability to 0.08. The search space for the shaping parameters is shown in Table 1.
[0135] S5. Experiments are conducted in each iteration. The six best data sets from the Pareto front solution set generated in each iteration are selected for the experiment. The manufactured part is 40mm in size. 3 ×3mm 3 ×20mm 3 Thin-walled wall and a size of 10mm 3 ×10mm 3 ×10mm 3 Blocks. Thin-walled walls are used for testing residual stress and deformation. Deformation is measured using vernier calipers (with a measurement accuracy of 5 μm), and residual stress is measured using X-ray diffraction. Blocks are also used for porosity testing; the porosity of the part is determined using the drainage method. Specific LPBF molded parts are shown below. Figure 3 As shown.
[0136] After four iterations of active learning, the final result was obtained. The value is 3.399%, so the iteration stops. The result generated by each active iteration is as follows: Figure 4 As shown. In the results of the last iteration, the result with the lowest Z value is selected as the result of the shaping parameters and target performance after active learning combined with multi-objective optimization.
[0137] The forming parameter combination obtained in Example 1 is as follows: laser power 132W, scanning speed 762mm / s, scanning spacing 0.101mm, scanning line length 1.81mm, interlayer rotation angle 67.6°, support tooth height 1.2mm, support tooth top width 1.42mm, and support tooth root width 1.75mm.
[0138] Meanwhile, the combination given in the TA15 titanium alloy forming parameter package recommended by the LPBF forming equipment was set as the actual production combination, in which the laser power was 190W, the scanning speed was 1050mm / s, the scanning interval was 0.1mm, the scanning line length was 5mm, the interlayer rotation angle was 67°, the support tooth height was 1mm, the support tooth top width was 1mm, and the support tooth root width was 1.5mm.
[0139] The porosity, residual stress, and deformation of the LPBF-formed part and the actual part were measured. The actual part had a measured porosity of 1.4%, a maximum residual stress of 728 MPa, and a maximum deformation of 0.315 mm. The LPBF-formed part had a porosity of 0.52%, a maximum residual stress of 485.5 MPa, and a maximum deformation of 0.188 mm.
[0140] Next, the tensile strength, elongation, fracture toughness, impact toughness, and fatigue cycle of the two samples were measured.
[0141] The tensile test rate was set to 1 mm / min, and the test was completed at room temperature.
[0142] Impact toughness was determined using the Charpy impact test, and the notch in the part was machined into a "V" shape.
[0143] Fracture toughness was determined according to the HB-5261-2023 standard for plane stress fracture toughness of the specimens.
[0144] Fatigue performance was tested under a pressure of 500 MPa.
[0145] The tensile strength and elongation results obtained from the multi-objective optimized part and the actual part were 1315.8 MPa and 1274.3 MPa, respectively, and 7.7% and 5.3%, respectively. Figure 5 As shown. The impact toughness and fracture toughness results are 27.19 J / cm. 2 and 19.59 J / cm 2 64.2 MPa·m 0.5 and 57.64 MPa·m 0.5 ,like Figure 6 As shown. The fatigue cycles are 8.2 × 10⁻⁶. 6 Zhou and 3.7×10 5 This demonstrates that the performance of the multi-objective optimized part in Example 1 is superior to that of the actual manufactured part, proving the effectiveness of this multi-objective optimization method.
[0146] Example 2
[0147] The operation steps are the same as in Example 1, except that in Example 2, the lowest Z value among the Z values other than those in Example 1 is selected from the results of the last iteration (the 4th iteration) for subsequent performance measurement and comparison. The purpose is to prove by comparison that the performance combination selected in Example 1 is the best performance combination.
[0148] The parameter combination selected in Example 2 is as follows: laser power 127W, scanning speed 1130mm / s, scanning spacing 0.089mm, scanning line length 1.31mm, interlayer rotation angle 72.1°, support tooth height 2.3mm, support tooth top width 1.39mm, and support tooth root width 1.94mm.
[0149] The porosity, residual stress, and deformation of the multi-objective optimized part were measured using the same test method as in Example 1. In Example 2, the porosity of the multi-objective optimized part was 0.64%, the maximum residual stress was 506.1 MPa, and the maximum deformation was 0.189 mm.
[0150] Next, the tensile strength, elongation, fracture toughness, impact toughness, and fatigue cycle of the multi-objective optimized component were tested using the same testing method as in Example 1. In Example 2, the tensile strength of the multi-objective optimized component was 1304.6 MPa, and the elongation was 7.1%. Figure 5 As shown. The impact toughness is 25.18 J / cm. 2 The fracture toughness is 62.3 MPa·m. 0.5 ,like Figure 6 As shown. The fatigue cycle is 8 × 10. 6 This indicates that the performance of the multi-objective optimized part is superior to that of the actual manufactured part in Example 1, proving the effectiveness of this multi-objective optimization method.
[0151] Example 3
[0152] The operation steps are the same as in Example 1, except that in Example 3, the lowest Z value among the Z values other than those in Example 1 and Example 2 is selected from the results of the last iteration (the 4th iteration) for subsequent performance measurement and comparison. The purpose is to prove by comparison that the performance combination selected in Example 1 is the best performance combination.
[0153] The parameter combination selected in Example 3 is as follows: laser power 126W, scanning speed 1102mm / s, scanning spacing 0.066mm, scanning line length 1.35mm, interlayer rotation angle 86.5°, support tooth height 2.35mm, support tooth top width 1.53mm, and support tooth root width 1.64mm.
[0154] The porosity, residual stress, and deformation of the multi-objective optimized part were measured using the same test method as in Example 1. In Example 3, the porosity of the multi-objective optimized part was 0.62%, the maximum residual stress was 504.7 MPa, and the maximum deformation was 0.207 mm.
[0155] Next, the tensile strength, elongation, fracture toughness, impact toughness, and fatigue cycle of the multi-objective optimized component were tested using the same testing method as in Example 1. In Example 3, the tensile strength of the multi-objective optimized component was 1306.2 MPa, and the elongation was 7.3%. Figure 5 As shown. The impact toughness is 25.66 J / cm. 2 The fracture toughness is 62.9 MPa·m. 0.5 ,like Figure 6 As shown. The fatigue cycle is 8 × 10. 6 This demonstrates that the performance of the multi-objective optimized part in Example 3 is superior to that of the actual manufactured part, proving the effectiveness of this multi-objective optimization method.
[0156] After comparison, the part in Example 1 showed the best performance and was determined as the final multi-objective optimization result. This also demonstrates the feasibility and efficiency of the multi-objective optimization method for LPBF parameter optimization based on the NSGA-II algorithm in this invention.
[0157] This invention addresses the problem of difficulty in controlling deformation and cracking in LPBF part parameter optimization due to the lack of comprehensive multi-objective collaborative optimization of stress, deformation, and density. It proposes an optimization strategy integrating machine learning and multi-objective evolutionary algorithms. Through the NSGA-II algorithm combined with active learning experimental iterations, a multi-parameter collaborative optimization framework is constructed, achieving efficient optimization of forming process parameters. Experimental results show that the parameter combinations obtained through this method improve part performance, overcome the lack of multi-parameter optimization methods in existing LPBF forming processes, improve material development efficiency, and provide a systematic solution for LPBF process parameter optimization.
[0158] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A multi-objective optimization method for LPBF parameter optimization based on the NSGA-II algorithm, characterized in that, Includes the following steps: S1. Establish a dataset and divide the dataset into a training set and a test set; wherein the training set and the test set each independently contain forming parameters and part performance, and the part performance includes multiple target performances; S2, using the training set to construct multiple prediction models corresponding to each target performance; S3, Evaluate the multiple prediction models using the test set to obtain the best prediction model for each target performance; S4, the optimal prediction model for multiple target performances is optimized using a second-generation non-dominated sorting genetic algorithm to generate a Pareto front and obtain multi-objective optimization results; the multi-objective optimization results include multiple sets of data, each set of data independently containing shaping parameters and multiple target performances; S5, Active Iterative Optimization: Experiment with the n optimal data sets from the multi-objective optimization results, and feed the experimental results back to the dataset. Perform multiple active iterative optimizations to obtain the optimal solution.
2. The multi-objective optimization method as described in claim 1, characterized in that, In step S1, the creation of the dataset includes: S1-1, Data Acquisition: The forming parameters that affect the target performance are screened out, and the correlation between the forming parameters is verified by using the Pearson correlation coefficient as a correlation analysis index. Then, the data of the relevant forming parameters and the target performance are collected. S1-2, Data preprocessing: Clean the data, perform min-max standardization on the data, and divide the data into the training set and the test set in an 8:2 ratio.
3. The multi-objective optimization method as described in claim 2, characterized in that, In step 1-1, the method for verifying correlation using the Pearson correlation coefficient includes: The formula for calculating the Pearson correlation coefficient is as follows: In the formula, x i and y i Let x represent the values of the two variables in the i-th sample of the dataset. a and y a This represents the average of two variables, x and y, across all samples in the dataset. Preferably, the correlation is verified using the Pearson correlation coefficient |r|. When |r| is -1, it indicates that the two variables x and y have a perfectly negative correlation; or, When |r| is 0, it indicates that there is no significant linear correlation between the two variables x and y; or, When |r| is 1, it indicates that the two variables x and y are perfectly positively correlated; Specifically, when |r| is less than or equal to 0.95, it indicates that the two forming parameters are not strongly correlated, so the corresponding forming parameter is retained; when |r| is greater than 0.95, it indicates that the two forming parameters are strongly correlated, so the forming parameter with the best prediction accuracy is retained, and the other is discarded.
4. The multi-objective optimization method as described in claim 2, characterized in that, In steps 1-2, all data obtained after cleaning are normalized using the min-max method: In the formula, x norm The standardized value, x i For the original data of a certain feature, x max and x min These represent the maximum and minimum values of the original feature data, respectively.
5. The multi-objective optimization method as described in claim 1, characterized in that, In step S2, the method for constructing the multiple prediction models includes: S2-1 uses seven regression algorithms in machine learning—SVR, RF, DT, GBDT, XGBoost, LGBM, and MLP—as well as the Python language to train the training set and obtain seven initial models. S2-2, using Bayesian optimization and 5-fold cross-validation, the hyperparameters of the seven initial models are optimized to obtain the seven prediction models.
6. The multi-objective optimization method as described in claim 1, characterized in that, In step S3, the evaluation method for the multiple prediction models includes: The forming parameters from the test set are input into the multiple prediction models to obtain multiple model prediction performance values. The multiple prediction models are evaluated by calculating the mean absolute error, root square error, and coefficient of determination of each model prediction performance value relative to the corresponding target performance value. The model with the smallest mean absolute error and / or square root error and the coefficient of determination closest to 1 is selected as the optimal prediction model.
7. The multi-objective optimization method as described in claim 1, characterized in that, Step S4, which involves optimizing the best prediction model for multiple target performances using a second-generation non-dominated sorting genetic algorithm, includes: S4-1 sets the search space for the objective function, relevant parameters, and corresponding shaping parameters. The relevant parameters include the population size, number of iterations N, crossover probability, and mutation probability. S4-2, perform the calculation of the second-generation non-dominated sorting genetic algorithm; Preferably, the number of iterations N is 100.
8. The multi-objective optimization method as described in claim 7, characterized in that, In step S4-2, the calculation steps of the second-generation non-dominated sorting genetic algorithm include: S4-2-1, by screening non-dominated individuals layer by layer and assigning incremental non-dominated levels until the entire population is stratified, a rapid non-dominated sorting is completed; S4-2-2, Calculate individual crowding degree, prioritize individuals with higher crowding degree to diversify the population and promote the even distribution of individuals of the same non-dominant level in the target space. The crowding degree calculation formula is: In the formula: L[i] d L[i+1] represents the crowding distance of individual i. m Let m be the function value representing the m-th objective of the (i+1)-th individual; and These are the maximum and minimum values of the m-th objective function in the set; S4-2-3: Select superior individuals from the population using non-dominated ordination and calculated crowding, generate new populations through crossover and mutation, and merge the populations. S4-2-4: Repeat steps S4-2-1 to S4-2-3 N times to complete N iterations of calculation, generate a Pareto front, and generate multi-objective optimization results.
9. The multi-objective optimization method as described in claim 1, characterized in that, In step S5, the steps of active iterative optimization are as follows: S5-1, normalize the performance of all objectives in multiple sets of objective optimization results to eliminate data scale differences, and calculate the evaluation function Z based on the normalized values. The calculation formula is as follows: In the formula: POR * RS * DFM * These are the normalized mapping values of the three objective values of porosity, residual stress, and deformation in the Pareto front, respectively. The Z value represents the comprehensive performance of the multi-objective optimization results in the solution set. S5-2: Sort the multiple sets of data in the multiple sets of objective optimization results, select the data set with the lowest function value, and obtain the forming parameter combination of the data set; based on the forming parameter combination, perform actual LPBF titanium part forming, test the porosity, residual stress and deformation of the part, add the value back to the training set, train the best prediction model again, and then repeat step S4 to perform the next multi-objective optimization. S5-3, take the optimized result as the result of one active iteration, and repeat steps S5-1 and S5-2 to perform multiple active iterations; S5-4, Calculate the average Z-value of the multiple data sets obtained in each iteration. The improvement rate, when Stop iteration when the improvement rate of the value is less than 5%; S5-5: In the Pareto front of the last active iteration, the data set with the lowest Z value is selected as the optimal solution.
10. The multi-objective optimization method as described in claim 1, characterized in that, The forming parameters include process parameters, scanning strategy, and support structure; wherein, the process parameters include laser power, scanning speed, and scanning spacing; the scanning strategy includes scanning line length, interlayer rotation angle, and support tooth height; and the support structure includes support tooth top width and support tooth root width. The performance of the component includes three target properties: porosity, residual stress, and deformation.