Adaptive sampling neural network model construction method suitable for SLM process optimization

Abstract

The application is a kind of adaptive point adding neural network model construction method suitable for SLM process optimization. It includes the following steps: (1) generating candidate set C through Sobol sequence, selecting initial data set M from candidate set C, establishing initial neural network model according to initial data set M and training; (2) dividing the entire variable value space X according to the approximate tesselation polygon method, obtaining the normalized design size calculation data of the tesselation polygon sample proportion of each existing sample point in the entire value space, calculating the leave-one-out cross-validation error of each sample point in data set M, and calculating the area needing to add points according to the tesselation polygon sensitivity formula; (3): adding points to the tesselation polygon sensitive area to obtain the updated data set M; (4): re-establishing the regression model and training. The application can effectively improve the engineering design optimization efficiency and shorten the design cycle.

Description

Technical Field

[0001] This invention belongs to the field of SLM additive manufacturing process parameter optimization, specifically involving an adaptive point-addition neural network model construction method suitable for SLM process optimization. Background Technology

[0002] Selective laser melting (SLM) is a widely used metal additive manufacturing process. However, due to its rapid heating and cooling process, the temperature gradient between different heat transfer zones is very large, resulting in extremely uneven distribution of thermal stress. This leads to quality problems in the printed parts, such as deformation, warping, air gaps, and cracks. To address these issues, domestic and international researchers have found that using appropriate process parameters (such as laser power, scanning speed, and scanning diameter) can adjust the thermal stress distribution, improve the quality of SLM-formed parts, and enhance their mechanical properties. Currently, companies using SLM technology to solve these problems mainly rely on the experience of technicians and conduct numerous parameter combination experiments by constantly adjusting equipment process parameters to obtain barely acceptable formed parts. However, this method results in a significant waste of manpower, materials, and equipment. More seriously, in many experiments, the inability to find a suitable combination of process parameters leads to the abandonment of SLM manufacturing. This patent proposes an adaptive point-addition strategy neural network regression model construction method to explore the optimal combination strategy for SLM parameters.

[0003] Before building a regression model, constructing a concentrated, effective, and typical dataset is crucial. The distribution of the sample points largely determines the accuracy of the trained model. A uniform distribution of sample points provides the model with better global information, accelerating model training and optimization. If the sample points are unevenly distributed, the collected model information is relatively scarce, leading to insufficient model accuracy or even modeling failure. A consensus is that the sample points in the dataset should obtain as much information as possible about the relationship between the target response and the design variables with as few trials as possible.

[0004] Traditional experimental design methods such as Latin hypercube consider the uniformity of sample point distribution in the variable value space, but they do not take into account the multidimensional complexity of practical engineering application problems and do not consider the error feedback problem when establishing surrogate models. Therefore, this method performs poorly in solving multidimensional nonlinear objective optimization designs using SLM, posing a huge challenge to the surrogate model establishment cycle and accuracy of SLM technology. Summary of the Invention

[0005] The purpose of this invention is to provide an adaptive point-addition neural network model construction method suitable for SLM process optimization.

[0006] The technical solution for achieving the objective of this invention is: an adaptive point-addition neural network model construction method suitable for SLM process optimization, comprising the following steps:

[0007] Step (1): Generate a candidate set C using the Sobol sequence, select the initial dataset M from the candidate set C according to the minimum-maximum distance criterion, build the initial neural network model based on the initial dataset M and train it;

[0008] Step (2): Divide the entire variable value space X into existing sample points in dataset M according to the method of approximating Thiessen polygons, and obtain the normalized design size of the proportion of Thiessen polygon samples of each existing sample point in the entire value space.

[0009] Calculate the leave-one-out cross-validation error for each sample point in dataset M.

[0010] Calculate the area that needs to be added using the Thiessen polygon sensitivity formula;

[0011] Step (3): Add points to the sensitive region of the determined Thiessen polygon using a parallel point-adding strategy to obtain the updated dataset M;

[0012] Step (4): Rebuild and train the regression model based on the updated dataset M in step (3), and verify the model accuracy. If the accuracy is satisfied, the neural network regression model is completed; if the accuracy is not satisfied, return to step (2).

[0013] Furthermore, in step (1), the number of sample points in the candidate set C is 1000q, where q is the dimension of the SLM parameter variable; the number of initial sample points added to the initial dataset M is N = 15q.

[0014] Furthermore, in step (1), q = 5 represents five design variables in the SLM process parameters, namely scanning strategy, laser power, overlap ratio, scanning speed and slice thickness.

[0015] Furthermore, the step (1) of selecting the initial dataset M from the candidate set C according to the minimum-maximum distance criterion is specifically as follows:

[0016] The first sample point added is randomly selected, and the remaining points are added according to the minimum-maximum distance criterion. The formula for adding the initial 15q sample points to the dataset M is expressed as:

[0017]

[0018] in It refers to the sample points selected from the candidate set C and added to the dataset M. X is any sample point in the candidate set C. i These are existing sample points in dataset M.

[0019] Furthermore, step (2) specifically includes the following steps:

[0020] Step (21): Calculate the Euclidean distance from each sample point in the candidate set C to the existing initial sample points in the dataset M; the calculation formula is as follows:

[0021] dom(M i M j )={M∈C|||MM i ||≤||MM j ||}

[0022] T i =dom(M i M j )

[0023] Where dom(M) i M j ) is the existing sample point M i and M j The hyperplane formed by the perpendicular bisector of the connecting lines, where M is the center point of the Thiessen polygon.

[0024] The sample points in the candidate set C with the closest Euclidean distance are assigned to the initial sample points M. The ratio of the number of points in each initial sample point region to the total number of points is used as the area size, i.e., the normalized design size of the proportion of the Thiessen polygon sample of each existing sample point in the entire value space.

[0025] Step (22): Perform leave-one-out cross-validation on each sample point in dataset M and calculate the validation error of each model.

[0026] Step (23): Calculate the area where points need to be added using the Thiessen polygon sensitivity formula, which is expressed as follows:

[0027]

[0028] In the formula, k is the weight, which is used to adjust the ratio between the two.

[0029] Furthermore, step (3) specifically involves:

[0030] For the Thésen polygon sensitive regions where points have been determined, a parallel point addition strategy is adopted. x polygons with the highest sensitivity index are selected at one time, and t sample points are added at a time. The first Thésen polygon point addition region is added with new sample points according to the minimum and maximum distance. When adding subsequent sample points, all samples in the dataset M are recalculated and added according to the minimum and maximum distance criterion.

[0031] Compared with the prior art, the significant advantages of this invention are:

[0032] This invention combines the uniformity of parameter value spatial distribution and the error of numerical model in the SLM process parameter optimization design process. It aims to achieve a balance between global and local distribution in the selection of SLM parameter sample points. Global distribution means considering the uniformity of SLM parameter value sample distribution throughout the variable value space; local distribution means considering the error after model training and supplementing sample points in the SLM nonlinear parameter region to reduce surrogate model error. This invention selects neural networks, which have strong data processing capabilities for nonlinear problems, as the regression model. It is more suitable for solving high-dimensional design parameter problems and can effectively improve the efficiency of engineering design optimization and shorten the design cycle. Attached Figure Description

[0033] Figure 1 This is a flowchart of the model construction method of the present invention.

[0034] Figure 2 The diagram shows a comparison between random sampling and Sobol sequence sampling in this invention; (a) is random sequence sampling, and (b) is Sobol sequence sampling.

[0035] Figure 3 A schematic diagram of adding points to the two-dimensional parameter variable value space.

[0036] Figure 4 The approximate Thiessen polygons are partitioned by sampling the two-dimensional parameter variable value space; where (a) is the distribution of points in the candidate set C after calculating the Euclidean distance, and (b) is the Thiessen polygons partitioned by the polygon estimation method.

[0037] Figure 5 This is an example of two-dimensional parameters for subsequent point additions.

[0038] Figure 6 The results are the test function results under different weights k.

[0039] Figure 7 The result of the test function for the number of points added in a single iteration. Detailed Implementation

[0040] The present invention will now be described in further detail with reference to the accompanying drawings.

[0041] An adaptive point-addition strategy neural network regression model based on SLM process optimization is proposed. First, a candidate set C is generated using Sobol sequences for the five process parameters of SLM. Then, an initial dataset M is selected from the candidate set according to the minimum-maximum distance. An initial neural network model is then built based on the selected dataset M to perform a regression model. Finally, based on dataset M, the entire design space is partitioned into the variable value space X using the principle of von Rohn's diagram, resulting in an approximate Thiessen polygon-Thiessen polygon spatial size. This serves as a criterion for sample sparsity. Simultaneously, leave-one-out cross-validation is performed on the existing sample points in dataset M to obtain the normalized validation error for each initial sample point. This serves as the model validation error. Next, using multiple test functions in the formula for determining the Thiessen polygon, a weight k = 0.7 was determined. Adding 5 sample points at a time shortens the modeling time and provides higher accuracy, making it more suitable for optimizing five-dimensional nonlinear parameters in SLM. The two errors are combined with the weight k and calculated to obtain the sensitivity index W for each Thiessen polygon. i This process determines the Thiessen polygons that need additional points, adds points according to the minimum-maximum distance criterion, calculates the response values ​​of newly added samples, updates the dataset M, rebuilds the regression model, and trains it until a neural network regression model that meets the accuracy requirements is obtained. Figure 1 This is a flowchart of the method for constructing a neural network regression model based on an adaptive point addition strategy optimized by SLM process, as described in this invention.

[0042] Figure 2 This is a comparison chart showing the distribution of 500 SLM parameter sample points generated by random sequences and Sobol sequences in two-dimensional space. It can be seen that the sample points from the random sequence are unevenly distributed, with local blank or clustered areas. In contrast, the Sobol sequence sampling exhibits better uniformity and variation. This uniformity avoids duplicate sampling between sample points, resulting in a higher quality sample point distribution.

[0043] by Figure 3The following example illustrates a point-addition design based on the minimum-maximum distance concept for two-dimensional parameter variables. Five sample points are taken from the two-dimensional variable value space, with each square representing a point in the candidate set. First, point P1 is randomly added. The distances from the remaining 24 squares to point P1 are calculated, and the point P2, with the largest distance (farthest from P1), is selected and added. Then, the distances from the remaining 23 points to P1 and P2 are calculated, for example, P3 and P3'. The distances from P3 to P1 and P2 are 3.162 and 4.125 respectively, and the distances from P3' to P1 and P2 are 3.00 and 3.162 respectively. The minimum value of each is selected as the feature distance; that is, the feature distance of P3 is 3.162, and the feature distance of P3'' is 3.00. Therefore, the point P3 with the largest minimum distance is added to the dataset. Subsequent points P4 and P5 are added using the same method of calculating feature distances. This sampling method effectively satisfies the requirement of uniform spatial distribution of the initial sample points for SLM parameter variables.

[0044] Taking the initial 8 sample points in the dataset as an example, in the design of the two-dimensional parameter variable value space, Figure 4 In (a), the large black dots represent the center points of the dataset. The regions of different shades of color are actually data spaces formed by dividing the N sample points in the candidate set C according to Thiessen polygons. Figure 4 In (b), the black lines represent the actual regions obtained according to the Thiessen polygons. A comparison shows that the boundaries of (a) and (b) are quite similar. To quantify the spatial size of each Thiessen polygon, the size of each region is obtained by dividing the number of sample points in each Thiessen polygon by the total number of sample points N in the candidate set. From the perspective of sample spatial distribution, the more sample points a Thiessen polygon has, the sparser the sample point distribution. More sample points should be added to such sparse regions to obtain more model information.

[0045] To add points to the defined Thiessen polygon regions, a parallel point-adding scheme is considered because the initial sample points are few. Adding a single point at a time would be time-consuming. This involves adding several points sequentially to accelerate model training. The main idea behind parallel point addition is the minimum-maximum distance approach: ① For the first added point, since the Thiessen polygons have already been defined, ensuring the distance from each point within the region to its center is minimized, the first point is added in the Thiessen polygon region with the highest sensitivity, using the maximum distance from the center. ② Subsequent sample points should calculate the distance between existing sample points in the dataset and the newly added first point, adding them using the minimum-maximum distance approach, rather than the same method as the first added point. Otherwise, issues may arise. Figure 5In this case, three target regions are selected, the first point is added according to the maximum distance, the second point is added according to the same method, but the newly added third point is also added according to the maximum distance point in the region. This is not good for establishing a multi-parameter nonlinear model of SLM, as the first point is too close and the two points contain similar model information.

[0046] In order to make reasonable choices about the value of weight k, and to balance the sparsity criterion of the variable value space X and the cross-validation error, test analysis was performed using a test function. Figure 6 These are the test function results under different weights k. In the stage where the number of samples is approximately 40 to 120, the root mean square error of the model decreases relatively quickly. However, as the number of sample points gradually increases, the rate of decrease in the root mean square error slows down. This indicates that the model has a poor fit to local nonlinear problems at this point, and it is necessary to increase the number of local sample points to improve the accuracy of the model. Therefore, when k is greater than 0, the validation error of sample points is taken into account. The validation error of the model in the later stage is significantly better than that in the early stage when only the global distribution uniformity is considered.

[0047] Adding new data samples to SLM using a single, incremental addition method results in significant computational resource waste and a lengthy training cycle. Therefore, adding multiple sample points at a time effectively improves sampling efficiency and shortens training time. This study tested the model by adding one, three, and five sample points at a time. Figure 7 This is the result of a test function for the number of points added in a single iteration. While the impact of each added point on the error during model training varies, all effectively improve the model's accuracy. Furthermore, adding multiple points at once significantly shortens the training cycle compared to adding a single new sample point. Adding five points at once has a more pronounced effect on improving the accuracy of this high-dimensional model. This is a crucial time cost factor in SLM parameter combination optimization design.

Claims

1. A method for constructing an adaptive point-addition neural network model suitable for SLM process optimization, characterized in that, The steps include the following: Step (1): Generate a candidate set C using the Sobol sequence, select the initial dataset M from the candidate set C according to the minimum-maximum distance criterion, build the initial neural network model based on the initial dataset M and train it; Step (2): Divide the entire variable value space X into existing sample points in dataset M according to the method of approximating Thiessen polygons, and obtain the normalized design size of the proportion of Thiessen polygon samples of each existing sample point in the entire value space. ; Calculate the leave-one-out cross-validation error for each sample point in dataset M. ; Calculate the area that needs to be added using the Thiessen polygon sensitivity formula; Step (3): Add points to the sensitive region of the determined Thiessen polygon using a parallel point-adding strategy to obtain the updated dataset M; Step (4): Rebuild and train the regression model based on the updated dataset M in step (3), and verify the model accuracy. If the accuracy is satisfied, the neural network regression model is completed; if the accuracy is not satisfied, return to step (2). In step (1), the number of sample points in the candidate set C is 1000q, where q is the dimension of the SLM parameter variable; the number of initial sample points added to the initial dataset M is N=15q; In step (1), q=5 represents five design variables in the SLM process parameters, namely scanning strategy, laser power, overlap ratio, scanning speed and slice thickness. Step (2) specifically includes the following steps: Step (21): Calculate the Euclidean distance from each sample point in the candidate set C to the existing initial sample points in the dataset M; the calculation formula is as follows: ， in Existing sample points and The hyperplane formed by the perpendicular bisector of the connecting lines. The center point of the Thiessen polygon. The sample points in the candidate set C with the closest Euclidean distance are assigned to the initial sample points M. The ratio of the number of points in each initial sample point region to the total number of points is used as the area size, i.e., the normalized design size of the proportion of the Thiessen polygon sample of each existing sample point in the entire value space. ; Step (22): Perform leave-one-out cross-validation for each sample point in the dataset M, and calculate the validation error for each model. ; Step (23): Calculate the area where points need to be added using the Thiessen polygon sensitivity formula, as shown in the formula below: ， In the formula It is a weight, used to adjust the ratio between the two.

2. The method according to claim 1, characterized in that, Step (1) involves selecting the initial dataset M from the candidate set C according to the minimum-maximum distance criterion, specifically as follows: The first sample point added is randomly selected, and the remaining points are added according to the minimum-maximum distance criterion. The formula for adding the initial 15q sample points to the dataset M is expressed as: ， in It refers to the sample points selected from the candidate set C and added to the dataset M. It is any sample point in the candidate set C. These are existing sample points in dataset M.

3. The method according to claim 2, characterized in that, Step (3) is as follows: For the Thésen polygon sensitive regions where points have been determined, a parallel point addition strategy is adopted. x polygons with the highest sensitivity index are selected at one time, and t sample points are added at a time. The first Thésen polygon point addition region is added with new sample points according to the minimum and maximum distance. When adding subsequent sample points, all samples in the dataset M are recalculated and added according to the minimum and maximum distance criterion.

4. The method according to claim 3, characterized in that, Weight k=0.7.

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