Multi-workpiece parallel 3D printing time prediction method based on machine learning fusion model

Abstract

The present application relates to a multi-workpiece parallel 3D printing time prediction method based on a machine learning fusion model, relates to the field of 3D printing technology and machine learning fusion, and comprises the following steps: collecting multi-workpiece parallel 3D printing data, performing pretreatment, and then standardizing to form a standardized data set; constructing a feature correlation probability model based on a Bayesian network structure learning and maximum likelihood estimation method; mining potential correlations between features in the standardized data set based on the feature correlation probability model to generate correlated features; screening the generated correlated features to form a final feature set; constructing a LightGBM model, and based on the final feature set, establishing a basic model for multi-workpiece parallel 3D printing time prediction after Bayesian optimization; overcoming the problems of imperfect feature engineering, insufficient model hyperparameter optimization and low prediction accuracy in existing multi-workpiece parallel 3D printing time prediction methods, and improving the accuracy and stability of multi-workpiece parallel 3D printing time prediction.

Description

Technical Field

[0001] This invention relates to the field of 3D printing technology and machine learning integration, specifically a method for predicting the time of multi-workpiece parallel 3D printing based on a machine learning fusion model. It is applicable to the accurate prediction of printing time in multi-workpiece parallel 3D printing scenarios, providing technical support for 3D printing production scheduling, cost control and efficiency optimization. Background Technology

[0002] 3D printing technology, as a core technology of additive manufacturing, has been widely used in aerospace, medical, and automotive fields due to its advantages such as mold-free production and customizable manufacturing. With the continuous increase in production demands, parallel 3D printing of multiple workpieces has become an important way to improve production efficiency. However, during parallel printing of multiple workpieces, printing time is affected by various factors, such as the geometric parameters of the workpieces (volume, surface area, complexity, etc.), printing process parameters (layer height, printing speed, infill rate, etc.), equipment parameters (nozzle temperature, platform temperature, etc.), and the layout parameters of the workpieces on the printing platform (spacing, arrangement, etc.), making it difficult to accurately predict printing time. Traditional 3D printing time prediction methods mainly include empirical formula methods and simple machine learning methods. Empirical formula methods are based on fitting a large amount of experimental data to obtain the relationship between printing time and related parameters, but this method can only consider a small number of key parameters and cannot fully cover the complex influencing factors in the scenario of parallel printing of multiple workpieces. Furthermore, it has poor generalization ability and large prediction errors in different scenarios. Simple machine learning methods, such as support vector machines and ordinary decision trees, can consider more parameters, but in the feature engineering stage, they often rely on manual selection or simple statistical methods to generate features, making it difficult to explore the potential correlations between features. At the same time, the model hyperparameters often rely on manual experience to adjust, which cannot guarantee the optimal performance of the model, resulting in prediction accuracy and stability that are difficult to meet the needs of actual production.

[0003] Other existing technologies, such as Chinese patent CN112380716B, disclose a method and system for estimating SLA 3D printing time based on a learning algorithm. This method is based on the SLA process and is not applicable to other 3D printing technologies. It requires a large amount of historical data to train the time deviation coefficient, has poor adaptability to new materials and processes, and is not designed for multi-task scenarios. Another Chinese patent, CN109648856B, discloses a method for estimating the processing time of a 3D printer. This method relies on standard part simulation, but the average speed assumption ignores individual differences, does not consider the synergistic effect of workpiece combinations, and cannot dynamically adjust the prediction results. Traditional methods cannot effectively handle spatial interference and thermodynamic coupling effects between workpieces, lack quantitative modeling of resource competition during multi-task parallel processing, do not consider the synergistic effect of workpiece combinations in feature engineering, and do not specifically tune hyperparameter optimization for multi-task scenarios. Summary of the Invention

[0004] The purpose of this invention is to overcome the problems of imperfect feature engineering, insufficient model hyperparameter optimization, and low prediction accuracy in existing multi-workpiece parallel 3D printing time prediction methods. It provides a multi-workpiece parallel 3D printing time prediction method based on machine learning fusion model, which improves the accuracy and stability of multi-workpiece parallel 3D printing time prediction and provides a reliable basis for 3D printing production management.

[0005] To address the aforementioned technical problems, this invention employs the following technical solution: a multi-workpiece parallel 3D printing time prediction method based on a machine learning fusion model, comprising the following steps:

[0006] Data from parallel 3D printing of multiple workpieces is collected, preprocessed, and then standardized to form a standardized dataset.

[0007] A feature association probability model is constructed based on Bayesian network structure learning and maximum likelihood estimation.

[0008] Based on a feature association probability model, latent associations between features in a standardized dataset are mined to generate associated features; and

[0009] The resulting associated features constitute the final feature set.

[0010] A LightGBM model was constructed, and a basic model for predicting the time of parallel 3D printing of multiple workpieces was established based on Bayesian optimization of the final feature set.

[0011] Preferably, the minimum sample size for a single scenario is calculated based on the statistical sample size, and the total sample size is obtained by combining the minimum sample size with the sample size collected in the actual scenario. The dataset covers multi-workpiece parallel printing scenarios with different workpiece types, different printing equipment models, and different production batches. The dataset includes workpiece geometric parameters, printing process parameters, and workpiece layout parameters.

[0012] Preferably, the preprocessing includes:

[0013] Missing value handling based on multiple imputation: Missing values ​​are statistically analyzed in the collected data, and the number of missing values ​​for each feature is calculated. For continuous features, imputation is performed using a regression model based on feature correlation. Correlation analysis is conducted by calculating the Pearson correlation coefficient between continuous features, and a multiple linear regression model is constructed. The trained multiple linear regression model is then used to fill in the missing values. For discrete features, imputation is performed using a class frequency-based method. The distribution frequency of each class in the samples without missing values ​​is statistically analyzed, and the missing values ​​are uniformly filled with the class with the highest frequency.

[0014] Box plot method, combined with 3D printing process constraints, is used to correct outliers: quartiles of each feature are calculated. and According to the formula Determine the outlier threshold; exclude values ​​smaller than 10 ... or greater than The sample was identified as an outlier; it was corrected by replacing the mean of adjacent samples, and the value was verified by process constraints.

[0015] Preferably, in the feature association probability model:

[0016] Using the feature vectors of the standardized dataset as input, the K2 algorithm is used to determine the structure of the Bayesian network. The feature nodes are sorted according to "geometric parameters → process parameters → layout parameters", and the Bayesian information criterion is used as the scoring function. By traversing the parent node combinations of the feature nodes, the maximum number of parent nodes is set to 3, and the network structure with the largest Bayesian information criterion value is selected as the optimal Bayesian network structure.

[0017] For each feature node in the optimal Bayesian network structure Based on its parent node The sample subsets are divided based on the combination of values; the conditional probability table of the Bayesian network is trained using the maximum likelihood estimation method to obtain the conditional probability distribution among features. ,in, Features The set of features of the parent node.

[0018] Preferably, the latent associations between features in the standardized dataset are mined based on a feature association probability model, specifically as follows:

[0019] For any two features and According to conditional probability Calculate the correlation coefficient between the two. The calculation formula is:

[0020] ;

[0021] in, For covariance, and are the standard deviations of the j-th and k-th features, respectively;

[0022] Feature pairs with an absolute correlation coefficient greater than 0.6 are selected to generate feature interaction terms. and ;

[0023] The workpiece geometric parameter group, printing process parameter group, and workpiece layout parameter group are divided into three groups of features respectively;

[0024] For each set of features, first, based on the posterior probability of the Bayesian network... Filtering effective features, among which As a dummy target variable, For features within a parameter group, PCA is used to reduce the dimensionality of each feature group, and the first three principal components are extracted as feature combination associated features.

[0025] Preferably, the filtering of related features includes:

[0026] The features in the standardized dataset are combined with the generated associated features to form the initial feature set. ;

[0027] The RFE method is used to process the initial feature set. Perform the screening;

[0028] Using the RMSE of the LightGBM model as the evaluation metric, features were progressively removed based on their contribution to model performance, retaining the top 20 features by importance to form the final feature set. .

[0029] Preferably, Bayesian optimization includes:

[0030] M sets of hyperparameter combinations are randomly sampled in the hyperparameter space, and LightGBM models are trained respectively. The objective function value corresponding to each set of hyperparameters is calculated to form the initial sample set.

[0031] Based on the initial sample set, the following operations are repeated until the number of iterations reaches a preset maximum number of iterations or the change in the objective function value is less than a preset threshold, resulting in a hyperparameter combination. The operations include:

[0032] GP is used as a surrogate model for Bayesian optimization. The GP model is fitted based on the initial sample set to obtain the probability mapping relationship between hyperparameters and objective function values.

[0033] The EI function is used as the Acquisition function to calculate the EI value of each candidate hyperparameter in the hyperparameter space;

[0034] Select the candidate hyperparameter combination with the largest EI value, train the LightGBM model and calculate its objective function value, add the hyperparameter combination and its objective function value to the sample set, and update the surrogate model.

[0035] Based on the obtained optimal hyperparameter combination, the LightGBM model is trained to build a basic model for predicting the time of multi-workpiece parallel 3D printing.

[0036] Preferably, the final feature set The corresponding dataset is divided into training and test sets. The CVRMSE of the LightGBM model on the training set with K-fold cross-validation is used as the objective function, and the goal is to minimize the CVRMSE.

[0037] Preferably, it also includes transfer learning of the base model, specifically:

[0038] For each scenario, sample data for that scenario is selected from the dataset to form a scenario dataset;

[0039] The transfer learning method is adopted, using the parameters of the basic model as prior knowledge, and fine-tuning the model based on the scene dataset, adjusting the learning rate and setting the training rounds;

[0040] After fine-tuning, a prediction model adapted to the specific scenario is obtained.

[0041] Preferably, for each scenario-adapted prediction model, a corresponding scenario test set is obtained from the scenario dataset, and the performance of the prediction model is verified using the test set. If the verification results meet the preset requirements, the scenario-adapted prediction model can be put into practical application; if not, the following operations are performed until the performance requirements are met:

[0042] Readjust the hyperparameter optimization range;

[0043] Increase the amount of sample data in this scenario;

[0044] Retrain the base model.

[0045] Beneficial effects: (1) This invention innovatively designs a feature association probability model using Bayesian network structure learning and maximum likelihood estimation. This feature association probability model can mine the potential association between features, generate feature interaction association features and feature combination association features, and combine the RFE method to screen high-quality features. It effectively solves the problems of incomplete feature information and insufficient association mining in traditional feature engineering, provides richer and more effective input features for the model, and improves the prediction basis of the model.

[0046] (2) This invention uses Bayesian optimization to optimize the hyperparameters of the LightGBM model. By constructing a GP surrogate model and an EI-based Acquisition function, the optimal combination of hyperparameters can be found in a smaller number of iterations. Compared with traditional hyperparameter optimization methods such as grid search and random search, this invention greatly improves the efficiency and accuracy of hyperparameter optimization and ensures the optimal performance of the LightGBM model.

[0047] (3) The method of the present invention also constructs an adaptive prediction model for different scenarios by performing transfer learning on the basic model. Compared with the traditional method, which requires training the model from scratch in a new scenario, the transfer learning strategy of the present invention has significant advantages. By loading the basic pre-trained model with initial parameters and combining it with a small number of new samples for model weight transfer and small sample fine-tuning, the model can better adapt to production scenarios with different workpiece types, different equipment models, and different batch sizes, thereby increasing the convergence speed in the new scenario by several times. This effectively solves the problems of poor generalization ability and large fluctuations in prediction accuracy in different scenarios of traditional models, and improves the applicability of the model in actual production.

[0048] (4) Through improved feature engineering and efficient hyperparameter optimization, combined with a scene adaptation model, the method of this invention has higher accuracy and stability in the prediction of time for parallel 3D printing of multiple workpieces. Experimental verification shows that compared with traditional empirical formula methods and simple machine learning methods, the RMSE of the method of this invention is reduced by 30%-50%. It improves the accuracy by 0.1-0.2, providing accurate and reliable time data for 3D printing production scheduling, cost estimation, and delivery planning, and has significant practical application value. Attached Figure Description

[0049] Figure 1 This is a flowchart illustrating the framework of the multi-workpiece parallel 3D printing time prediction method based on Bayesian optimization-LightGBM of this invention. Detailed Implementation

[0050] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0051] Example: Figure 1 As shown, the method for predicting the time of parallel 3D printing of multiple workpieces based on a machine learning fusion model includes the following steps:

[0052] S1. Collect parallel 3D printing data from multiple workpieces, preprocess the data, and standardize it to form a standardized dataset; specifically including:

[0053] S11. Define the implementation scenario: Construct a multi-dimensional production scenario system based on workpiece type, equipment model, and batch size;

[0054] S12. Determine the data acquisition scheme: Adopt a fusion strategy of full scene coverage and multiple batch repetition, and design the data acquisition scheme in combination with parameter types and physical logic. The acquired data mainly includes relevant data in the parallel 3D printing process of multiple workpieces. The specific data parameters are as follows:

[0055] Workpiece geometric parameters: Total volume of the workpiece Maximum volume of workpiece Minimum volume of workpiece Average volume of workpiece Maximum height of workpiece Minimum height of workpiece Average height of workpiece Total surface area Complexity ,in Calculated by the ratio of the number of triangular facets on the workpiece surface to the number of reference facets;

[0056] Printing process parameter data: layer height Printing speed Fill rate Nozzle temperature Platform temperature ;

[0057] Workpiece layout parameter data: lateral spacing of the workpiece on the printing platform Longitudinal spacing Number of rows Number of columns .

[0058] S121. Determine the parameter acquisition range: All parameter settings must strictly meet the physical constraints of the 3D printing process;

[0059] S122. Data acquisition equipment and tools: Use appropriate acquisition tools and equipment according to different parameters;

[0060] S123. Sample Size Design: Based on the statistical sample size calculation formula, as shown in the following formula, calculate the minimum sample size for a single scenario. :

[0061] ;

[0062] in, Let be the confidence interval. Standard deviation Allowable error;

[0063] Based on the minimum sample size and the sample size collected in the actual scenario, the total sample size N is obtained;

[0064] The collected data covers parallel printing scenarios of multiple workpieces with different workpiece types, different printing equipment models, and different production batches. To ensure the diversity and representativeness of the data, this invention collected a total of N sets of sample data, thus forming the original dataset D:

[0065] ;

[0066] in, Let be the feature vector of the i-th sample group. is the actual printing time for the i-th sample.

[0067] S13. Data Preprocessing: This mainly includes three steps: missing value handling, outlier handling, and data standardization. The specific steps are as follows:

[0068] S131. Missing Value Handling: This embodiment uses multiple interpolation to check for missing values. The specific steps are as follows:

[0069] a. Missing value detection: Count missing values ​​in the original dataset and calculate the number of missing values ​​for each feature;

[0070] b. Continuous feature imputation: For continuous features, the method of constructing a regression model based on feature correlation is used for imputation. Correlation analysis is performed by calculating the Pearson correlation coefficient between continuous features, a multiple linear regression model is constructed, and the trained model is used to fill in the missing values ​​to verify whether the filling accuracy meets the control requirements.

[0071] c. Discrete feature imputation: For discrete features, imputation is performed using a class frequency-based method. First, the distribution frequency of each class in the samples without missing values ​​is counted. Then, the missing values ​​are uniformly filled with the class with the highest frequency to ensure the stability of the data distribution.

[0072] S132. Outlier Handling: This embodiment uses the box plot method, combined with 3D printing process constraints, to correct outliers. Specifically, it includes three steps: quartile calculation, outlier identification, and outlier correction. The process is as follows:

[0073] a. Quartile calculation: Calculate the quartiles of each feature. (Lower quartile) and (Upper quartile), according to the formula Determine the threshold for outlier detection;

[0074] b. Outlier identification: Values ​​less than... or greater than The sample was identified as an outlier;

[0075] c. Outlier correction: The correction is performed by replacing the mean of adjacent samples, and the correction value is verified through process constraints to ensure that it is within a reasonable physical range.

[0076] S133. Data Standardization: To eliminate the influence of different feature dimensions, this embodiment uses the Z-score standardization method to standardize the preprocessed feature data, as detailed below:

[0077] a. Statistical calculation: For the dataset after outlier correction, calculate the mean of each feature along the feature dimension. and standard deviation ;

[0078] b. Standardization Calculation: The feature values ​​of each sample are standardized using the following formula:

[0079] ;

[0080] in, Let j be the original value of the j-th feature in the i-th sample group. Let be the mean of the j-th feature. Let be the standard deviation of the j-th feature. These are the standardized eigenvalues;

[0081] c. Standardization Validation: Verify that the mean and standard deviation of all standardized features meet the expected range, ensuring the elimination of the influence of units, thus obtaining the standardized dataset. ;

[0082] S2. Constructing a feature association probability model based on Bayesian network structure learning and maximum likelihood estimation, specifically including:

[0083] S211. Learning Bayesian network structures, the specific steps are as follows:

[0084] a. Using standardized datasets eigenvectors As input, the K2 algorithm is used to determine the structure of the Bayesian network, which is sorted according to "geometric parameters → process parameters → layout parameters". The feature node order is set as follows:

[0085] ;

[0086] The Bayesian Information Criterion (BIC) is used as the scoring function.

[0087] b. By traversing the possible combinations of parent nodes of the feature nodes, the maximum number of parent nodes is set to 3 to avoid overfitting due to excessive network complexity. The network structure with the largest BIC value is selected as the optimal Bayesian network structure.

[0088] S212. The specific steps of the maximum likelihood estimation method are as follows:

[0089] a. For each feature node in the optimal Bayesian network structure Based on its parent node The combinations of values ​​are used to divide the sample into subsets;

[0090] b. Based on the maximum likelihood estimation method, parameters are learned for the Conditional Probability Table (CPT) of the Bayesian network to obtain the conditional probability distribution among features. ,in Features The set of features of the parent node.

[0091] S22. Based on the constructed feature association probability model, the potential association relationships between features are mined, and associated features are generated. The specific steps are as follows:

[0092] S221. The specific steps for feature interaction and feature association are as follows:

[0093] a. For any two features and According to conditional probability Calculate the correlation coefficient between the two. The formula is as follows:

[0094] ;

[0095] in, For covariance;

[0096] b. Select feature pairs with an absolute correlation coefficient greater than 0.6 and generate feature interaction terms. and .

[0097] S222. The specific steps for feature combination and feature association are as follows:

[0098] a. Divide the workpiece geometric parameter group, printing process parameter group, and workpiece layout parameter group into three sets of features respectively. , and ;

[0099] b. For each set of features, the posterior probability is based on a Bayesian network. Select effective features, among which As a dummy target variable, The parameters are defined as features within a group. Then, PCA is used to reduce the dimensionality of each feature group and the first three principal components are extracted as feature combination association features.

[0100] S23. The feature selection method using Recursive Feature Elimination (RFE), LightGBM, and Root Mean Squared Error (RMSE) as evaluation is as follows:

[0101] S231. Combine the original standardized features with the generated associated features to form an initial feature set. .

[0102] S232. RFE Filtering Parameter Settings: Use the RFE method to filter the initial feature set. Perform the screening.

[0103] S233. Using the RMSE of the LightGBM model as the evaluation metric, features that contribute little to the model's performance are gradually eliminated, retaining the top 20 features by importance to form the final feature set. ;

[0104] S3. Construct the LightGBM model, and based on the final feature set, establish a basic model for predicting the time of multi-workpiece parallel 3D printing after Bayesian optimization. Specifically, this includes:

[0105] S31. Dataset Partitioning and Model Initialization: This invention partitions the dataset and initializes the model according to the 7:3 partitioning and stratified sampling rules. The specific steps are as follows:

[0106] S311. Final feature set The corresponding dataset is divided into a training set and a test set, and in this embodiment, the ratio is 7:3.

[0107] The basic parameters of the S312.LightGBM model include the learning rate. The tree count is num_leaves, the maximum tree depth is max_depth, the minimum sample weight and min_child_weight required for a leaf node are min_child_weight, the subsample ratio is subsample, and the column sample ratio is colsample_bytree;

[0108] S32. Determine the hyperparameters of LightGBM to be optimized and their value ranges;

[0109] S33. Using the CVRMSE of the LightGBM model on the training set (K-fold cross-validation) as the objective function, the goal is to minimize the CVRMSE. The objective function expression is as follows:

[0110] ;

[0111] in, For cross-validation folds, The actual printing time for the i-th fold and j-th sample is... Let be the printing time for the model's prediction of the j-th sample in the i-th fold. Let be the number of samples in the i-th fold;

[0112] S34. The specific steps for Bayesian optimization of hyperparameters are as follows:

[0113] S341. Randomly sample M sets of hyperparameter combinations in the hyperparameter space, train the LightGBM model respectively, calculate the objective function value corresponding to each set of hyperparameters, and form an initial sample set;

[0114] S342. Gaussian Processes (GP) are used as surrogate models for Bayesian optimization. The GP model is fitted based on the initial sample set to obtain the probability mapping relationship between hyperparameters and objective function values.

[0115] S343. Using the Expected Improvement (EI) function as the Acquisition function, calculate the EI value of each candidate hyperparameter in the hyperparameter space. The larger the EI value, the greater the potential of the candidate hyperparameter to improve the current optimal objective function value.

[0116] S344. Select the candidate hyperparameter combination with the largest EI value, train the LightGBM model and calculate its objective function value, add the hyperparameter combination and its objective function value to the sample set, and update the surrogate model.

[0117] S345. Repeat the steps of constructing the surrogate model, calculating the Acquisition function, and updating hyperparameters until the number of iterations reaches the preset maximum number of iterations or the change in the objective function value is less than the preset threshold. The hyperparameter combination obtained at this point is the optimal hyperparameter combination.

[0118] ;

[0119] S35. Use the optimal hyperparameter combination obtained in step S345. The LightGBM model was trained based on the training set to obtain the basic model for predicting the time of parallel 3D printing of multiple workpieces. .

[0120] S4. Perform transfer learning on the base model, specifically:

[0121] S41. Scene Segmentation: Based on the actual production scenario of multi-workpiece parallel 3D printing, the scene is segmented according to three dimensions: workpiece type, printing equipment model, and production batch scale, resulting in... Different scenarios, denoted as ;

[0122] S42. Scene Adaptation Model Training (Transfer Learning): The specific implementation steps are as follows:

[0123] S421. Initial Parameter Loading: For each scenario Sample data for this scenario are selected from the dataset to form the scenario dataset. Based on the basic model obtained in step S3 This is the initial model;

[0124] S422. Fine-tuning parameter settings: Using transfer learning, the parameters of the base model are used as prior knowledge, based on the scene dataset. Fine-tune the model by adjusting the learning rate and setting the number of training epochs;

[0125] S423. Fine-tuning: Perform fine-tuning operations to obtain a scenario-adapted prediction model. ;

[0126] S43. Model Performance Verification and Optimization:

[0127] S431. Performance Metric Calculation: For a specific scenario (i.e., when i=k), calculate the performance metrics from the scenario dataset. The model was divided into a 7:3 ratio to obtain corresponding scene test sets. These test sets were used to validate the model's performance, employing RMSE, mean absolute error (MAE), and coefficient of determination (COP). The model performance is evaluated using three indicators, and the evaluation formula is as follows.

[0128] ;

[0129] ;

[0130] ;

[0131] in, This represents the number of samples in the scenario test set. To determine the actual printing time of the i-th sample in the test set, Let be the printing time for the model's prediction of the i-th sample. This represents the average actual printing time for the test set.

[0132] S432. Model Optimization: If the model performance metrics meet the preset requirements, then the prediction model adapted to this scenario is... If the requirements are not met, return to step S3 and perform the following operations until the performance requirements are met:

[0133] a. Readjust the hyperparameter optimization range;

[0134] b. Increase the amount of sample data in this scenario;

[0135] c. Retrain the model.

[0136] This application also provides a specific embodiment that comprehensively analyzes the above-mentioned multi-workpiece parallel 3D printing time prediction method based on Bayesian optimization-LightGBM, as follows:

[0137] Taking a multi-workpiece parallel printing production line in a 3D printing factory as an application scenario, it covers two core workpiece types commonly used in the industrial manufacturing field: high-strength plastic workpieces (such as nylon structural parts, with a single workpiece weight of 0.3-4kg, which are suitable for the impact-resistant molding requirements of general 3D printing processes) and general plastic workpieces in the consumer electronics field (such as polylactic acid (PLA) shell parts, with a single workpiece weight of 5-45g, which are suitable for the requirements of fine structure and surface finish).

[0138] This embodiment uses three different models of 3D printers, namely device A, device B, and device C. Each device has significant differences in key process parameters such as maximum forming size, applicable material types, printing nozzle diameter, and applicable production scale, as shown in Table 1:

[0139] Table 1. Process parameters of three 3D printers

[0140]

[0141] Production batch sizes are divided into three levels based on the number of products: small batch (1–10 pieces), medium batch (11–50 pieces), and large batch (51 pieces or more).

[0142] Based on the above factors, a multi-dimensional production scenario system was constructed, which includes 2 types of workpieces, 3 equipment models, and 3 batch sizes, forming a total of 18 typical production scenarios.

[0143] The process parameters involved in this embodiment are set according to the standard specification "GB / T35024-2018 Additive Manufacturing Terminology" and are comprehensively determined in combination with the company's actual production statistics. The parameter value range covers the conventional production baseline value and the 15% boundary test value to effectively improve the robustness and generalization ability of the model. All parameter settings strictly meet the physical constraints of the 3D printing process;

[0144] In this embodiment, appropriate data acquisition tools and devices are used according to different parameters, as detailed below:

[0145] Workpiece geometric parameters: Using a high-precision 3D scanner, the measurement error of volume and surface area is ≤2%;

[0146] Printing process parameters: collected through the printer's built-in control system, with a sampling frequency of 1Hz, and real-time recording of parameters such as printhead temperature, platform temperature, and printing speed;

[0147] Actual printing time: Automatically timed by the control system with an accuracy of ±1 second. The timing range is from the completion of printhead preheating to the end of the last layer printing, eliminating interference from equipment standby time.

[0148] Workpiece layout parameters: Using a high-precision camera combined with OpenCV image recognition algorithm (error ≤ 0.1mm), the measurement was repeated twice and the average value was taken to reduce the error to ≤ 0.05mm;

[0149] In this embodiment, the confidence level is set to 1.96, the standard deviation is 0.15, and the allowable error is 0.05. According to the statistical sample size calculation formula, the minimum sample size for a single scenario is calculated to be 139 groups.

[0150] To ensure statistical significance, 200 valid samples were collected for each scenario (44% more than the minimum sample size); considering data redundancy and outlier removal requirements, 220 samples were actually collected for each scenario, for a total sample size of 18 × 220 = 3960 (18 typical production scenarios × 220 samples collected per scenario).

[0151] During the data collection process, the same parameter combination was printed three times, and the average of the actual printing times was taken as the target value t for that sample (standard deviation ≤ 5% to ensure data stability). This data constituted the original dataset. , where the feature vector ;

[0152] Using Python's Pandas library to process the original dataset To perform missing value statistics, the isnull().sum() function was used to calculate the number of missing values ​​for each feature. The results show... , , There are missing parameters, but the missing rate of other parameters is less than 5%, which is within the statistically acceptable range and no additional data collection is required.

[0153] For continuous features such as total volume V and printing speed v, imputation is performed using a regression model based on feature correlation. The specific steps are as follows:

[0154] The Pearson correlation coefficient between continuous features is calculated using the corr() function, with the total volume as the metric. For example, it is similar to (0.92) (0.88) (0.95) (0.85) (0.81) are all strongly correlated (|r|>0.8) and there is no multicollinearity (variance inflation factor VIF is less than 5), which meets the requirements for screening strong correlation features;

[0155] In terms of total volume With the dependent variable being the five strongly correlated features mentioned above, and the 3912 groups of samples without missing data (3960-48=3912 groups), the dataset was divided into a training set (2738 groups) and a validation set (1174 groups) in a 7:3 ratio. A multiple linear regression model was constructed using sklearn.linear_model.LinearRegression. =0.91 (high goodness of fit), RMSE=5.2cm³ (relative error ≤4.3%, based on...) (Calculated based on an average value of 120 cm³), which meets the accuracy requirements of the regression model;

[0156] Using the trained model to determine the total volume Forty-eight sets of missing values ​​were predicted and imputed. After imputation, the prediction error of the validation set was ≤3%, meeting the requirements for imputation accuracy control. Similarly, printing speed... interpolation model =0.89, RMSE=3.5mm / s (relative error ≤4.1%, based on...) (Calculated based on an average speed of 65 mm / s), the filling effect is good;

[0157] For discrete features, the specific steps are as follows:

[0158] Calculated using the value_counts(normalize=True) function The distribution frequency in samples without missing data is as follows: =2 (18%) =3 (25%) =4 (22%) =5 (15%) =1 (8%) =6-10 (12%), of which =3 has the highest frequency (which conforms to the common layout of equipment platforms, such as the width of A of the equipment is 300mm, and the width of each workpiece in 3 rows is ≤100mm, leaving sufficient spacing to avoid thermal deformation), which is consistent with the requirement of reasonable discrete feature distribution;

[0159] Will All 20 missing values ​​were filled with 3. The frequency variation of the distribution is ≤0.1%, ensuring that the distribution of discrete features has not shifted significantly, which is consistent with the logic of data stability after interpolation.

[0160] For the dataset after imputing missing values, the percentile() function in Python's NumPy library is used to calculate the percentile of each continuous feature. , and At printing speed For example, the calculation is as follows =45mm / s, =100mm / s, =55mm / s, the original outlier judgment threshold is mm / s (no practical significance, corrected to 20mm / s based on the minimum speed of 3D printing process of 20mm / s), mm / s (combined with the maximum process speed of 150 mm / s, corrected to 150 mm / s), the corrected threshold meets the requirements of physical constraint verification;

[0161] Statistical analysis revealed 42 anomalous samples in the dataset, accounting for 1.06% of the total sample size, which is consistent with the expected outlier rate of <2%. These anomalous samples were primarily concentrated in printing speed. Fill rate and complexity See Table 2:

[0162] Table 2 Abnormal Samples and Outliers

[0163]

[0164] For the identified abnormal samples, the replacement method based on the mean of adjacent samples is combined with process constraint verification and correction. The specific steps are as follows:

[0165] Take the mean features of 5 normal samples before and after the abnormal sample (a total of 10 samples), and calculate the value based on printing speed. Taking the abnormal sample as an example (index 125, =175mm / s), the first 5 samples The mean was 85 mm / s, and the last 5 samples The mean is 92 mm / s, so the average value is 88.5 mm / s;

[0166] Check whether the mean is within a reasonable physical range for this feature. The reasonable range is 20-150 mm / s. If 88.5 mm / s meets the requirements, it is used as the correction value. If the mean exceeds the range (e.g., the mean of an abnormal filling rate sample is 110%), the upper limit of the feature (100%) is taken as the correction value. After correction, the statistical indicators (mean, standard deviation) of each feature are recalculated. The difference from the original value is ≤1%, the data distribution is more reasonable, and all samples meet the requirements of the process constraints.

[0167] For the outlier-corrected dataset, calculate the mean of each feature along the feature dimension. and standard deviation This ensures that the statistics are based on the full valid sample. (Based on floor height) For example, =0.15mm, =0.06mm ( The range is 0.05-0.3 mm, with a reasonable standard deviation, reflecting the data dispersion; the total surface area is used as the basis for measurement. For example, =350cm², =120cm² (S ranges from 10 to 1000cm², with the mean and standard deviation matching and no extreme bias), consistent with the requirement that the statistic calculation is based on the full sample.

[0168] The feature values ​​of each sample are standardized using a standardized calculation formula, such as the layer height of a sample. =0.21mm, after standardization =(0.21-0.15) / 0.06=1.0 (within the interval [-3,3], there are no extreme standardized values); Total surface area of ​​a sample =590cm², after standardization =(590-350) / 120=2.0 (also within a reasonable range), all calculations conform to the formula definition;

[0169] After standardizing all samples, the standardized mean (which should be close to 0) and standard deviation (which should be close to 1) of each feature were checked. The results showed that the standardized mean of all features was between -0.05 and 0.05, and the standard deviation was between 0.95 and 1.05, which meets the requirements of Z-score standardization. This eliminates the model training bias caused by differences in units (such as volume in cm³ versus velocity in mm / s), resulting in a standardized dataset. .

[0170] With standardized datasets eigenvectors For the input (18 features), the K2 algorithm is implemented using Python's pgmpy library; the feature node order is set as follows. The maximum number of parent nodes is set to 3 (to avoid overfitting due to an overly complex network structure).

[0171] Using BIC as the scoring function, the formula is as follows:

[0172] ;

[0173] in, The likelihood function value, With a sample size of 3960, The number of model parameters;

[0174] This example: Learning When the parent node is tested, the combination is tested. (BIC=-1250) (BIC=-1320) (BIC=-1280) The maximum BIC (S reflects the number of surface details) (Affects the number of layers); learning When the parent node is combined (BIC=-1180) is optimal (layer height determines the printing area of ​​each layer, and fill rate determines the printing time of each layer, which together affect the speed selection); in the final structure, the correlation between geometric parameters, process parameters, and layout parameters is significant (BIC difference > 50), while the correlation between cross-type parameters is weak (BIC difference < 10), which is in line with the parameter influence law and verifies the rationality of the structure.

[0175] In this embodiment, printing speed For example, its parent node is ,Will The standardized value ranges [-3, -1], [-1, 1], and [1, 3] are divided into three categories: low-rise, mid-rise, and high-rise. Similarly, they are divided into three categories, forming a total of 3×3=9 combinations of parent node values, corresponding to 9 sample subsets (each subset has 350-450 samples, evenly distributed).

[0176] For each sample subset, the maximum likelihood estimation method is used to calculate... The formula is as follows:

[0177] ;

[0178] in, This represents the number of samples where the parent node takes value 'b' and the child node takes value 'a'. (The total number of samples for the parent node b).

[0179] In this implementation, the parent node is combined with " (Mid-rise) Within the subset of "(fill rate)", The sample size for the (medium speed) subset is 280, and the total sample size for this subset is 350. =280 / 350=0.8. All conditional probabilities are between 0 and 1, and the sum of the probabilities under each combination of parent nodes is 1, which satisfies the requirements of the probability axiom and provides a reliable foundation for the subsequent generation of associated features.

[0180] In this embodiment, the Pearson correlation coefficient is calculated based on the above formula: for example and of =0.91 (strong positive correlation; the larger the volume, the larger the surface area). and of =-0.72 (strong negative correlation; the smaller the floor height, the lower the speed is needed to ensure accuracy). and of =0.68 (moderate positive correlation, horizontal and vertical spacing is usually consistent in the layout). and of =0.15 (weak correlation, nozzle temperature and number of rows are not directly related), all coefficient calculation results conform to parameter correlation logic;

[0181] Feature pairs with an absolute correlation coefficient greater than 0.6 are selected to generate feature interaction terms. and A total of 42 groups were obtained. For each feature pair, two interaction features were generated: a multiplicative interaction term and an additive interaction term, resulting in a total of 42 × 2 = 84 feature interaction association features. For example, based on and ( =0.91) Generate " " ",based on and ( =-0.72) generates " " ".

[0182] Based on functional type, the features are divided into three groups, specifically including:

[0183] Workpiece geometric parameter set: (9 features);

[0184] Printing process parameter group (5 characteristics);

[0185] Workpiece layout parameter group (4 characteristics);

[0186] For each set of features, first, based on the posterior probability of the Bayesian network... Select effective features (posterior probability > 0.7) and then perform PCA dimensionality reduction;

[0187] With geometric parameter set For example, filter out (0.85) (0.92) (0.88) (0.81) (0.75) Five features; calculate the covariance matrix to obtain eigenvalues ​​3.2, 1.8, 0.9, 0.6, and 0.5. The cumulative contribution rate of the first three eigenvalues ​​is (3.2 + 1.8 + 0.9) / 7.0 ≈ 84.3% (≥80%, meeting the contribution rate requirement). Extract the first three principal components as... Group combination features , and ;

[0188] Similarly, process parameter group The cumulative contribution rate of the top three principal components was 82.1%, extracted as... , and Layout parameter group The cumulative contribution rate of the top three principal components was 85.7%, extracted as... , and A total of 3×3=9 feature combinations were generated to associate features.

[0189] Based on the above, this embodiment uses a feature selection method evaluated by RFE, LightGBM, and RMSE. The specific steps are as follows:

[0190] The original standardized features (18), feature interaction features (84), and feature combination features (9) are combined to form the initial feature set. The total number of dimensions is 18 + 84 + 9 = 111;

[0191] Implement the RFE algorithm using sklearn.feature_selection.RFE, with the following parameter settings:

[0192] Initial hyperparameters: estimator=LightGBM ( =0.1, num_leaves=31, max_depth=-1);

[0193] Select 20 optimal features: n_features_to_select=20;

[0194] Each time, remove the 5 features with the smallest contribution: step=5.

[0195] Train the initial LightGBM model and output feature importance scores, such as combined features. (0.12) Interaction Features (0.10) Original features (0.08) High score, original features (0.002), Interaction Features (0.001) Low score;

[0196] Each time, five low-importance features were removed, the model was retrained and the RMSE was calculated: the RMSE of the initial feature set of 111 features was 0.105, the RMSE of 20 features was 0.08, and the RMSE of 15 features was increased to 0.12, indicating that 20 features is the optimal dimension.

[0197] The first 20 features (6 original features + 10 interactive features + 4 combined features) are retained to form the final feature set. .

[0198] Will The corresponding dataset was divided into training and test sets in a 7:3 ratio. Stratified sampling was used based on scene labels to ensure that the sample ratio of each scene was consistent with the original dataset. There were a total of 3,600 valid samples (18 original scenes × 200 sets / scene). After the division, the training set had 2,520 sets (140 sets / scene) and the test set had 1,080 sets (60 sets / scene).

[0199] Initial parameters are set to =0.1, num_leaves=31, max_depth=-1, min_child_weight=1, subsample=0.8, colsample_bytree=0.8, objective="regression", metric="rmse", num_boost_round=100.

[0200] The hyperparameter ranges are set according to physical meaning and experimental experience, as shown in Table 3:

[0201] Table 3. Definition of hyperparameter space for Bayesian optimization

[0202]

[0203] Based on the above objective function formula, where K is taken as 5, There are 2520 / 5=504 groups, implemented using the Optuna library, ensuring that the mean is calculated after each subdivision to avoid error fluctuations.

[0204] In this embodiment, 20 sets of hyperparameter combinations are randomly sampled in the hyperparameter space, the model is trained and CVRMSE is calculated, the initial RMSE range is 0.075-0.112, and the optimal initial RMSE is 0.075.

[0205] In this embodiment, GP is used as the surrogate model, the RBF kernel function is selected, and the probability mapping relationship between hyperparameters and RMSE is obtained based on the initial sample fitting.

[0206] Calculate the Acquisition function: using the specified EI function, the formula is as follows:

[0207] ;

[0208] in, To predict the mean, Standard deviation To achieve the current optimal RMSE, , These are the cumulative distribution function and probability density function of the standard normal distribution, respectively.

[0209] The EI value is calculated by grid search, the candidate hyperparameter combination with the largest EI is selected, the LightGBM model is trained and its objective function value is calculated, the hyperparameter combination and its objective function value are added to the sample set, and the surrogate model is updated.

[0210] In this embodiment, the optimal hyperparameter combination is obtained after 50 iterations. : =0.06, num_leaves=78, max_depth=6, min_child_weight=3.2, subsample=0.88, colsample_bytree=0.82, corresponding CVRMSE=0.068, a 35.2% reduction compared to the initial model (RMSE=0.105).

[0211] The training process employs an early stop mechanism and training round control methods, using... Training the base model The `early_stopping_rounds` parameter was set to 10 (to avoid overfitting), and convergence occurred after 85 training epochs (early stopping was triggered). The test set validation results were RMSE = 0.071 and MAE = 0.052. =0.963, indicating strong generalization ability.

[0212] Based on the above, the implementation steps for adapting and validating prediction models in different scenarios are as follows:

[0213] The scenarios are primarily categorized based on three dimensions: workpiece type, equipment model, and batch size. Each scenario is named using scenario tags, such as "High-strength Plastics - Equipment A - Small Batch" and "General Plastics - Equipment B - Medium Batch," resulting in a total of 18 scenarios. Scenario datasets can be filtered by tags. It contains 200 sets of samples (140 sets for training and 60 sets for testing), and the feature distributions between scenes are significantly different (e.g., the average temperature of nozzle A is 235℃, and the average temperature of nozzle B is 200℃), which meets the requirements of scene specificity.

[0214] load The parameters are used as the initial parameters of the scene model to avoid training from scratch.

[0215] The learning rate is set to 0.1 times the base model ( =0.006), with 20 training rounds, and the fixed tree structure only updates the weights of the leaf nodes.

[0216] Each scene model is trained for 20 rounds, such as scene (High-strength plastic + Equipment A + small batch) After fine-tuning, the validation set RMSE = 0.045, resulting in 18 scene adaptation models. to .

[0217] Use the specified RMSE, MAE, Three indicators, 16 models, RMSE < 4.5%, >0.97 (meets preset requirements); 2 models (e.g.) (High-strength plastics + Equipment C + large-volume production) Initial RMSE = 0.058 =0.945 (not up to standard).

[0218] For substandard models, a strategy combining hyperparameter tuning and sample supplementation is adopted:

[0219] a. Adjust the range of hyperparameters: such as num_leaves max_depth Where num_leaves and max_depth ;

[0220] b. Increase the amount of sample data in this scenario: supplement with 50 sets of samples (the proportion of large batch samples increases to 60%).

[0221] c. Retrain the model: After fine-tuning... RMSE = 0.046 =0.981 (meets the standard).

[0222] Task Scenario Recognition: A production task scenario involves printing 15 sets of carbon fiber reinforced ABS high-strength plastic parts (medium batch). The parts are printed using equipment C. The scenario is matched with "high-strength plastic - equipment C - medium batch". The corresponding model is... (Test set RMSE=0.043, =0.982).

[0223] Feature data acquisition and preprocessing: Feature parameters need to be compared with feature vectors Consistency: =120cm³, =120cm³, =450cm² =0.2mm, =45mm / s, =70%, =250℃, =100℃, =12.5mm, =22.5mm, =3, =5; Process the feature data according to the data preprocessing method in step S1, and standardize it according to Z-score to obtain... (Dimension 20).

[0224] Prediction and Validation: This mainly includes two steps: prediction execution and actual validation. Specifically, firstly, enter The output standardized prediction value is 0.5, which is obtained through inverse standardization ( =4.0h, =0.8h) =4.4h, and finally, by comparing with the actual printing time of 4.35h, the relative error was found to be 1.2% (<5%), thus verifying the effectiveness of the model.

[0225] The above is a summary of the specific implementation methods of the present invention, and the implementation effects can be summarized from three main objectives: improved accuracy, scene adaptation, and engineering practicality.

[0226] (1) Improved prediction accuracy: The average RMSE of the scene model is 0.045 (<4.5%), which is 66.7% higher than the traditional empirical formula method (RMSE>15%) and 43.8% higher than the simple machine learning method (such as SVM, RMSE>8%), meeting the goal of "accurate prediction".

[0227] (2) Strong scene adaptability: It covers 18 scenarios, and expansion only requires 200 additional samples + 10 minutes of fine-tuning, which meets the needs of multi-scenario adaptation.

[0228] (3) High engineering practicality: No additional hardware investment is required. The model can be integrated into the MES system. Production efficiency is expected to increase by 15%-20%, and cost control accuracy will be improved by more than 20%, which is in line with the technical positioning of production scheduling and cost control support.

[0229] The above embodiments demonstrate that the method of this patent achieves the invention goal of accurately predicting the time of parallel 3D printing of multiple workpieces.

[0230] The embodiments of the present invention have been described in detail above with reference to the examples. However, the present invention is not limited to the above embodiments. For those skilled in the art, after learning the contents described in the present invention, several equivalent changes and substitutions can be made without departing from the principle of the present invention. These equivalent changes and substitutions should also be considered to fall within the protection scope of the present invention.

Claims

1. A method for predicting the time of parallel 3D printing of multiple workpieces based on a machine learning fusion model, characterized in that: Includes the following steps: Data from parallel 3D printing of multiple workpieces is collected, preprocessed, and then standardized to form a standardized dataset. A feature association probability model is constructed based on Bayesian network structure learning and maximum likelihood estimation; in the feature association probability model: Using the feature vectors of the standardized dataset as input, the K2 algorithm is used to determine the structure of the Bayesian network. The feature nodes are sorted according to "geometric parameters → process parameters → layout parameters", and the Bayesian information criterion is used as the scoring function. By traversing the parent node combinations of the feature nodes, the maximum number of parent nodes is set to 3, and the network structure with the largest Bayesian information criterion value is selected as the optimal Bayesian network structure. For each feature node in the optimal Bayesian network structure Based on its parent node The sample subsets are divided based on the combination of values; the conditional probability table of the Bayesian network is trained using the maximum likelihood estimation method to obtain the conditional probability distribution among features. in, Features The set of features of the parent node; Based on a feature association probability model, latent associations between features in a standardized dataset are mined to generate associated features; and The resulting associated features constitute the final feature set. A LightGBM model was constructed, and a basic model for predicting the time of parallel 3D printing of multiple workpieces was established based on Bayesian optimization of the final feature set.

2. The method for predicting the time of multi-workpiece parallel 3D printing based on a machine learning fusion model according to claim 1, characterized in that: The minimum sample size for a single scenario is calculated based on statistical sample size, and the total sample size is obtained by combining the minimum sample size with the sample size collected in the actual scenario. The dataset covers multi-workpiece parallel printing scenarios with different workpiece types, different printing equipment models, and different production batches. The dataset includes workpiece geometric parameters, printing process parameters, and workpiece layout parameters.

3. The method for predicting the time of multi-workpiece parallel 3D printing based on a machine learning fusion model according to claim 2, characterized in that: The preprocessing includes: Missing value handling based on multiple imputation: Missing values ​​are statistically analyzed in the collected data, and the number of missing values ​​for each feature is calculated. For continuous features, imputation is performed using a regression model based on feature correlation. Correlation analysis is conducted by calculating the Pearson correlation coefficient between continuous features, and a multiple linear regression model is constructed. The trained multiple linear regression model is then used to fill in the missing values. For discrete features, imputation is performed using a class frequency-based method. The distribution frequency of each class in the samples without missing values ​​is statistically analyzed, and the missing values ​​are uniformly filled with the class with the highest frequency. Box plot method, combined with 3D printing process constraints, is used to correct outliers: quartiles of each feature are calculated. and According to the formula Determine the outlier threshold; exclude values ​​smaller than 10 ... or greater than The sample was identified as an outlier; it was corrected by replacing the mean of adjacent samples, and the value was verified by process constraints.

4. The method for predicting the time of multi-workpiece parallel 3D printing based on a machine learning fusion model according to claim 3, characterized in that: The method for mining potential associations between features in a standardized dataset based on a feature association probability model is as follows: For any two features and According to conditional probability Calculate the correlation coefficient between the two. The calculation formula is: ； in, For covariance, and are the standard deviations of the j-th and k-th features, respectively; Feature pairs with an absolute correlation coefficient greater than 0.6 are selected to generate feature interaction terms. and ; The workpiece geometric parameter group, printing process parameter group, and workpiece layout parameter group are divided into three groups of features respectively; For each set of features, first, based on the posterior probability of the Bayesian network... Filtering effective features, among which As a dummy target variable, For features within a parameter group, PCA is used to reduce the dimensionality of each feature group, and the first three principal components are extracted as feature combination associated features.

5. The method for predicting the time of multi-workpiece parallel 3D printing based on a machine learning fusion model according to claim 4, characterized in that: Filtering related features includes: The features in the standardized dataset are combined with the generated associated features to form the initial feature set. ; The RFE method is used to process the initial feature set. Perform the screening; Using the RMSE of the LightGBM model as the evaluation metric, features were progressively removed based on their contribution to model performance, retaining the top 20 features by importance to form the final feature set. .

6. The method for predicting the time of multi-workpiece parallel 3D printing based on a machine learning fusion model according to claim 5, characterized in that: Bayesian optimization includes: M sets of hyperparameter combinations are randomly sampled in the hyperparameter space, and LightGBM models are trained respectively. The objective function value corresponding to each set of hyperparameters is calculated to form the initial sample set. Based on the initial sample set, the following operations are repeated until the number of iterations reaches a preset maximum number of iterations or the change in the objective function value is less than a preset threshold, resulting in a hyperparameter combination. The operations include: GP is used as a surrogate model for Bayesian optimization. The GP model is fitted based on the initial sample set to obtain the probability mapping relationship between hyperparameters and objective function values. The EI function is used as the Acquisition function to calculate the EI value of each candidate hyperparameter in the hyperparameter space; Select the candidate hyperparameter combination with the largest EI value, train the LightGBM model and calculate its objective function value, add the hyperparameter combination and its objective function value to the sample set, and update the surrogate model. Based on the obtained optimal hyperparameter combination, the LightGBM model is trained to build a basic model for predicting the time of multi-workpiece parallel 3D printing.

7. The method for predicting the time of multi-workpiece parallel 3D printing based on a machine learning fusion model according to claim 6, characterized in that: The final feature set The corresponding dataset is divided into training and test sets. The CVRMSE of the LightGBM model on the training set with K-fold cross-validation is used as the objective function, and the goal is to minimize the CVRMSE.

8. The method for predicting the time of multi-workpiece parallel 3D printing based on a machine learning fusion model according to claim 1, characterized in that: This also includes transfer learning of the base model, specifically: For each scenario, sample data for that scenario is selected from the dataset to form a scenario dataset; The transfer learning method is adopted, using the parameters of the basic model as prior knowledge, and fine-tuning the model based on the scene dataset, adjusting the learning rate and setting the training rounds; After fine-tuning, a prediction model adapted to the specific scenario is obtained.

9. The method for predicting the time of multi-workpiece parallel 3D printing based on a machine learning fusion model according to claim 8, characterized in that: For each scenario-adapted prediction model, a corresponding scenario test set is obtained from the scenario dataset. The performance of the prediction model is verified using the test set. If the verification results meet the preset requirements, the scenario-adapted prediction model can be deployed in practical applications. If not, the following operations are performed until the performance requirements are met: Readjust the hyperparameter optimization range; Increase the amount of sample data in this scenario; Retrain the base model.

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