Digital light processing 3D printing precision improvement method based on random forest algorithm

Abstract

The present application relates to the technical field of 3D printing precision improvement method, more specifically to a digital light processing 3D printing precision improvement method based on random forest algorithm. For the reverse design strategy based on interpretable learning, the parameter backstepping and optimization under the target curing precision are realized by adopting the following scheme: measuring under different exposure times, fitting the curve according to the Jacob work curve equation; changing I, calculating the under different light intensity; designing a test structure to quantify the printing effect under different parameters; selecting appropriate parameter range for printing; observing and measuring the size through a microscope, and constructing a data set; linearly normalizing the data set, and dividing it into a training set and a test set in proportion; training a random forest model. The optimal printing parameters are obtained by using the trained model, and printing is carried out, the printed structure size is measured and added to the data set, the model is retrained until the key size error meets the standard.

Description

Technical Field

[0001] This invention relates to the technical field of 3D printing accuracy improvement methods, and more specifically to a digital light processing 3D printing accuracy improvement method based on the random forest algorithm. Background Technology

[0002] In high-precision digital light processing (DLP) 3D additive manufacturing, exposure parameters (including light intensity, exposure time, layer thickness, etc.) have a significant impact on photopolymerization behavior and printing accuracy. Due to the complex nonlinear coupling relationships between factors such as light absorption, polymerization rate, and light scattering in photocurable resins, traditional parameter adjustments relying on experience or trial-and-error methods are often inefficient and struggle to balance cured dimensional accuracy and printing stability. Furthermore, while traditional modeling methods based on empirical formulas or single-factor designs (such as Jacobs models or response surface methodology) can describe the relationship between curing depth and energy density, their predictive accuracy and scalability are limited in scenarios with multi-parameter coupling, high-dimensional variables, and significant material variations.

[0003] With the rise of data-driven approaches in manufacturing, machine learning models have been introduced to reveal the nonlinear mapping relationship between complex photopolymer 3D printing parameters and curing characteristics. Among these, Random Forest (RF), a nonparametric model based on ensemble learning, possesses advantages such as high robustness, strong anti-overfitting ability, and good interpretability, enabling effective prediction of curing accuracy with limited experimental data. By constructing a regression model between printing parameters and curing width and its error, high prediction accuracy can be obtained with fewer experiments, further revealing key factors affecting printing accuracy and providing a theoretical basis for subsequent parameter optimization and control.

[0004] However, predictive models can only establish "forward" relationships, that is, predict the printing result from given parameters. In practical applications, the "reverse" problem is more valuable: how to automatically derive the optimal combination of printing parameters based on the desired curing accuracy or structural characteristics. Although traditional optimization algorithms (such as genetic algorithms and Bayesian optimization) can achieve some reverse design functions, they usually rely on a large number of iterative calculations, which are inefficient and lack interpretability, and still need to be improved. Summary of the Invention

[0005] This invention provides a method for improving the accuracy of digital light processing 3D printing based on the random forest algorithm. The purpose is to propose a reverse design strategy based on interpretable learning to achieve parameter back-calculation and optimization under the target solidification accuracy.

[0006] The above objectives are achieved through the following technical solutions:

[0007] A method for improving the accuracy of digital light processing in 3D printing based on the random forest algorithm includes the following steps:

[0008] S1: Select the resin type for the test structure, fix the exposure power I, design the test structure unit, and measure the actual thickness of the cured resin layer under different exposure times. According to the Jacob working curve equation , fitting - Curves are used to calculate the parameter-based curing penetration depth. and the energy required for polymerization ;

[0009] S2: Change I to calculate different light intensities. and ;

[0010] S3: Design a dedicated test structure to quantify the printing effects of different exposure power, exposure time, and layer thickness printing parameters;

[0011] S4: Select the parameter range based on the experimental objectives and equipment performance, and then print.

[0012] S5: Print the structure according to the set parameters, observe and measure the dimensions using a microscope, and construct a structure including light intensity (I), exposure time (T), layer thickness (H), and designed linewidth (…). ), measured line width ( ) and the calculated curing error ( = - The dataset;

[0013] S6: Perform linear normalization on the dataset, mapping the input variables to the [0,1] interval, and divide it into training and test sets in a 4:1 ratio;

[0014] S7: Train the random forest model and adjust the hyperparameters by the number of decision trees and the number of feature subsets at each split. The split criteria for the trees are Gini impurity or minimum mean square error, and the minimum number of samples for the leaf nodes is set to 1.

[0015] S8: Use the trained model to obtain the optimal printing parameters and print, measure the size of the printed structure and add it to the dataset, then retrain the model;

[0016] S9: Repeat S8 until the critical dimension error meets the standard.

[0017] The test structure is a three-layer stepped micro-nano drag reduction structure, which includes an optimized texture formed by multi-level geometric superposition based on the fractal concept on the basis of the classic trench drag reduction structure.

[0018] The dedicated test structure consists of six parallel layers, each containing 10 test structure units. The line width of the structure units increases in increments of 10 μm from 10 μm to 100 μm. All structure units have the same length, and adjacent lines maintain a fixed spacing.

[0019] The printing parameters are as follows: UV light intensity 5–120 mW / cm², exposure time selected using a decreasing gradient method (15s, 10s, 5s, and 2.5s), and layer thickness selected (10μm, 20μm, and 40μm).

[0020] The optical microscope is used to measure the size of the sample. Each sample is measured multiple times and the average value is taken. The microscopic image is then processed for background light correction and contrast normalization. Measurement points with uneven local exposure or edge defects are removed and replaced with the average value of adjacent samples.

[0021] In S5, the dataset is stored in a standardized format, and all variables are input as normalized values. Data precision is retained to three decimal places. Outlier detection is performed on each set of measurement data, and box plots are used to identify outliers that deviate from the main distribution. If the deviation exceeds 3... If the percentage of data with (standard deviation) is greater than 5%, then the sample group should be remeasured.

[0022] The mean absolute error and coefficient of determination are used as performance evaluation indicators for the model. When the MAE is close to 1 and relatively small, the model is considered to have acceptable prediction accuracy and stability, and the model performs well on the test set. The value should be kept above 0.90, and the MAE should be controlled below 1.5 μm. MAE measures the average deviation between the predicted and actual values. To evaluate the model's ability to explain the population variance.

[0023] The robustness of the model was evaluated using a 5-fold cross-validation method.

[0024] Formula for calculating the performance evaluation index of the model:

[0025]

[0026]

[0027] In the formula: These are experimental measurements. These are the model's predicted values. is the sample mean, and n is the total number of test samples.

[0028] The beneficial effects of the digital light processing 3D printing accuracy improvement method based on the random forest algorithm of this invention are as follows:

[0029] Optimized test structure design lays a solid foundation for high-quality data: The innovative design of a three-layer stepped micro-nano drag-reducing test structure unit, as well as a dedicated test structure consisting of six parallel layers with 10 test structure units per layer, not only makes the energy distribution more uniform during the printing process and the measurement results more statistically significant, but also allows for the direct acquisition of 60 sets of solidified data with different feature sizes in a single print run. This effectively quantifies the improvement in printing accuracy and provides sufficient, comprehensive, and high-quality data support for the training of random forest models, solving the problems of limited data volume and poor statistical properties in traditional test structures.

[0030] The algorithm selection is highly adaptable, and the prediction accuracy and stability are excellent: The random forest algorithm is used to construct the exposure parameter-curing response model. As a nonparametric model based on ensemble learning, this algorithm has the core advantages of high robustness, strong anti-overfitting ability and good interpretability. It can accurately characterize the comprehensive influence of multiple parameters on curing width in the case of limited experimental data, and achieve effective prediction of curing accuracy. It avoids the defects of insufficient prediction accuracy of traditional empirical formulas or single-factor design models in the case of multi-parameter coupling and high-dimensional variables.

[0031] Innovative reverse design strategy to meet core practical application needs: Based on the forward prediction model, a reverse design strategy based on interpretable learning is further proposed. By leveraging the interpretability and probabilistic output characteristics of the model, the core function of inferring the optimal combination of printing parameters from the target fixed accuracy or structural features is realized. This breaks through the limitation of the traditional forward prediction model that can only "guess the result from the parameters". At the same time, it solves the problems of large iterative computation, low efficiency and poor interpretability of traditional reverse optimization algorithms (such as genetic algorithms and Bayesian optimization), which are more in line with the application needs of "customized accuracy on demand" in actual production.

[0032] A robust measurement and data mechanism ensures model reliability and iterative accuracy: By using multiple instruments to jointly measure the geometric features and curing width of the printed sample, both measurement accuracy and data comprehensiveness are taken into account. At the same time, a data preprocessing, outlier detection, quantitative evaluation of model performance, and closed-loop data update mechanism are established. This not only ensures the accuracy of model reliability evaluation and the reusability of data, but also drives the printing accuracy to continuously approach the target value by continuously incorporating new data, updating the model and optimal parameters, and achieving dynamic improvement in accuracy.

[0033] The system framework is complete and closed-loop, providing comprehensive technical support: This invention constructs a complete system framework of "experimental data acquisition - model construction - parameter prediction - reverse design - experimental verification", which organically integrates data acquisition, model training, parameter optimization, effect verification and other links to form a closed-loop iterative process. It can systematically solve the precision control problem caused by multi-parameter coupling in DLP photopolymerization printing, and provide comprehensive and feasible theoretical and methodological support for high-precision control and intelligent optimization of DLP photopolymerization printing. Attached Figure Description

[0034] Figure 1 The diagram shows the three-layer stepped micro / nano drag reduction structure, its cross-section, and its dimensions.

[0035] Figure 2 This image shows an enlarged view of the three-layer stepped micro / nano drag-reduction structure.

[0036] Figure 3 The image shows a super depth-of-field measurement of a three-layer stepped micro / nano drag-reduction structure.

[0037] Figure 4 The Jacobs fitting curve is shown;

[0038] Figure 5 A diagram of the dedicated test structure is shown;

[0039] Figures 6 to 14 The graph showing the results of the printing error measurement is displayed. Detailed Implementation

[0040] A method for improving the accuracy of digital light processing in 3D printing based on the random forest algorithm includes the following steps:

[0041] Step 1: Select the resin type. Choose HTL (general purpose resin) from Mofang Precision. Its coefficient of thermal expansion is 169 µm / m / C at temperatures between 50℃ and 100℃, and 143 µm / m / C at 100℃ and 150℃. HTL's heat distortion temperature under a 0.45 MPa load is 114℃. This resin effectively improves single-point exposure accuracy and curing uniformity, thus ensuring the fidelity of printing complex microstructures.

[0042] Step Two: The test structure unit is designed as a three-layer stepped micro / nano drag-reduction structure. This structure is an optimized texture formed by multi-level geometric superposition based on the classic trench drag-reduction structure and incorporating fractal concepts. Specifically, such as... Figure 1 As shown, the dimensions of each position of the structure are determined using design software based on the cross-sectional view of the structure. Figure 2 This is a magnified image of the actual object. Figure 3 This is a super-depth-of-field measurement map.

[0043] Step 3: (1) Fix the exposure power I and change the exposure time. Measure the actual thickness of the cured resin layer under different exposure times. ;

[0044] (2) According to Jacob (Jacobs working curve, i.e.) - Model) Working curve equation, Fitting - Curves are used to calculate the curing penetration depth under different light intensities. and the energy required for polymerization .

[0045] (3) Change the exposure power I to obtain multiple sets The data is shown in Table 1 below, used to calculate different light intensities. and :

[0046]

[0047] Step Four: As Figure 5 As shown, a dedicated overall test structure is designed, consisting of six parallel layers, each containing 10 test structure units.

[0048] Specifically, the structural units are arranged with line widths increasing sequentially in increments of 10µm, from 10µm to 100µm. All structural units maintain a consistent length, and adjacent lines are kept at a fixed spacing.

[0049] Step 5: Set the ultraviolet light intensity range to 5–120 mW / cm²;

[0050] Exposure time was determined using a decreasing gradient method, with 15s, 10s, 5s, and 2.5s selected within a total time interval of 15s; layer thicknesses were selected as 10µm, 20µm, and 40µm. The process parameters are shown in Table 1 below.

[0051] Process parameters type Minimum value Maximum value Exposure power density (mW / cm2) variable 5 120 Exposure time (s) variable 0.1 20 Layer thickness (µm) variable 10 40 Alcohol cleaning time (min) Quantitative 3 / Printing temperature (°C) Quantitative 25 / Post-curing time (s) Quantitative 30 /

[0052] Step 5: Using an optical microscope (such as Keyence VHX-7000), the overall structure of the sample is observed at low magnification and preliminary dimensional measurements are performed to obtain the curing linewidth distribution under different energy parameters. The optical microscope has a magnification range of 50–2000x and a resolution of up to 0.5 µm, allowing for rapid measurement under non-destructive conditions. Specifically, the printed structure is thoroughly rinsed with anhydrous ethanol and air-dried at room temperature for 24 hours. Finally, the dimensions are measured, marked, and recorded using an optical microscope. Each sample is measured three times, and the average value is taken to form the average curing width data under a single parameter combination. To improve data consistency, background light correction and contrast normalization are performed on each microscopic image. Normalization is a maximum-minimum normalization, which maps pixel values ​​from the original 0-255 range to the [0,1] interval through linear scaling. If there are local exposure imbalances or edge defects in the image, the measurement point is discarded and replaced with the average of adjacent samples. The red curve represents the ideal printing width; the closer the data is to the red line, the smaller the actual printing error. The measurement results are as follows: Figures 6 to 14 As shown.

[0053] Step Six: The dataset parameters are light intensity (I), exposure time (T), layer thickness (H), and design linewidth (…). ), measured line width ( ) and the calculated curing error ( = - The dataset is divided into training and test sets in a 4:1 ratio. Specifically, the dataset is stored in a standardized format, with variables input as normalized values ​​and data precision retained to three decimal places. To ensure data quality, outlier detection is performed on each set of measurements. Box plots are used to identify outliers deviating from the main distribution; if the deviation exceeds 3... If the percentage of data with (standard deviation) is greater than 5%, then the sample group should be remeasured.

[0054] Step 7: The random forest model is tuned using two key hyperparameters: the number of decision trees (n_estimators) and the number of feature subsets at each split (max_features). Cross-validation is performed with multiple parameter combinations, and the parameter set with the best model performance is selected as the final settings. The splitting criterion for each tree uses Gini impurity or minimum mean squared error (MSE) as the optimization objective, and the minimum number of samples per leaf node is set to 1.

[0055] Random forests generate [data] by performing random sampling with replacement on the sample set. Different subsample sets And train a decision tree on each subset of samples. When splitting nodes, each tree does not use all features, but randomly selects m features from all features for splitting judgment, in order to increase the difference between trees.

[0056] Step 8: The performance evaluation metrics for the model are Mean Absolute Error (MAE) and Coefficient of Determination (R²), calculated using the following formulas:

[0057]

[0058]

[0059] In the formula:

[0060] —Experimental measurements;

[0061] —Model predictions;

[0062] —Sample mean;

[0063] n—the total number of test samples;

[0064] MAE – Measures the average deviation between predicted and actual values;

[0065] —Evaluate the model's ability to explain the population variance.

[0066] when A value close to 1 and a small MAE indicate that the model has good prediction accuracy and stability. The model's fitting ability can be intuitively evaluated by comparing the predicted values ​​with the actual measured values ​​on the test set. To further quantify the model performance, the MAE and MAE values ​​of the training and test sets were calculated. The values ​​and results show the model's performance on the test set. 2 All values ​​remained above 0.90, and the MAE was controlled below 1.5 µm, indicating that the model has excellent generalization ability and prediction accuracy. Furthermore, cross-validation was used to evaluate the model's robustness, with each fold... The small fluctuation range indicates that the model training did not exhibit overfitting.

Claims

1. A method for improving the accuracy of 3D printing using digital light processing based on the random forest algorithm, characterized in that, Includes the following steps: S1: Select the resin type for the test structure, fix the exposure power I, design the test structure unit, and measure the actual thickness of the cured resin layer under different exposure times. According to the Jacob working curve equation , fitting - Curves are used to calculate the parameter-based curing penetration depth. and the energy required for polymerization ; S2: Change I to calculate different light intensities. and ; S3: Design a dedicated test structure to quantify the printing effects of different exposure power, exposure time, and layer thickness printing parameters; S4: Select the parameter range based on the experimental objectives and equipment performance, and then print. S5: Print the structure according to the set parameters, observe and measure the dimensions using a microscope, and construct the structure including light intensity I, exposure time T, layer thickness H, and designed linewidth. Measured line width and the calculated curing error = - The dataset; S6: Perform linear normalization on the dataset, map the input variables to the [0,1] interval, and divide it into training and test sets in a 4:1 ratio; S7: Train the random forest model and adjust the hyperparameters by the number of decision trees and the number of feature subsets at each split. The split criteria for the trees are Gini impurity or minimum mean square error, and the minimum number of samples for the leaf nodes is set to 1.

2. The method for improving the accuracy of 3D printing using digital light processing based on the random forest algorithm according to claim 1, characterized in that, it also... include: S8: Use the trained model to obtain the optimal printing parameters and print, measure the size of the printed structure and add it to the dataset, then retrain the model; S9: Repeat S8 until the critical dimension error meets the standard.

3. The method for improving the accuracy of 3D printing using digital light processing based on the random forest algorithm according to claim 2, characterized in that, The test structure is a three-layer stepped micro-nano drag reduction structure, which includes an optimized texture formed by multi-level geometric superposition based on the fractal concept on the basis of the classic trench drag reduction structure.

4. The method for improving the accuracy of 3D printing using digital light processing based on the random forest algorithm according to claim 1, characterized in that, The dedicated test structure consists of six parallel layers, each containing 10 test structure units. The line width of the structure units increases in increments of 10 μm from 10 μm to 100 μm. All structure units have the same length, and adjacent lines maintain a fixed spacing.

5. The method for improving the accuracy of 3D printing using digital light processing based on the random forest algorithm according to claim 1, characterized in that, The printing parameters are as follows: UV light intensity 5–120 mW / cm², exposure time selected using a decreasing gradient method (15s, 10s, 5s, and 2.5s), and layer thickness selected (10μm, 20μm, and 40μm).

6. The method for improving the accuracy of 3D printing using digital light processing based on the random forest algorithm according to claim 1, characterized in that, The optical microscope is used to measure the size of the sample. Each sample is measured multiple times and the average value is taken. The microscopic image is then processed for background light correction and contrast normalization. Measurement points with uneven local exposure or edge defects are removed and replaced with the average value of adjacent samples.

7. The method for improving the accuracy of 3D printing using digital light processing based on the random forest algorithm according to claim 6, characterized in that, In S5, the dataset is stored in a standardized format, and all variables are input as normalized values. Data precision is retained to three decimal places. Outlier detection is performed on each set of measurement data, and box plots are used to identify outliers that deviate from the main distribution. If the deviation exceeds 3... If the proportion of data is greater than 5%, then the sample group should be remeasured.

8. The method for improving the accuracy of 3D printing using digital light processing based on the random forest algorithm according to claim 2, characterized in that, Mean absolute error and coefficient of determination are used as performance metrics for the model on the test set. A model is considered to have acceptable prediction accuracy and stability when its accuracy is maintained above 0.90 and its mean square error (MAE) is controlled below 1.5 μm. Here, MAE measures the average deviation between predicted and actual values. To evaluate the model's ability to explain the population variance.

9. The method for improving the accuracy of 3D printing using digital light processing based on the random forest algorithm according to claim 8, characterized in that, The robustness of the model was evaluated using a 5-fold cross-validation method.

10. The method for improving the accuracy of 3D printing using digital light processing based on the random forest algorithm according to claim 8, characterized in that, Formula for calculating the performance evaluation index of the model: In the formula: These are experimental measurements. These are the model's predicted values. is the sample mean, and n is the total number of test samples.

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