Experimental Study and Random Forest Machine Learning of Surface Roughness for a Typical Laser Powder Bed Fusion Al Alloy

Abstract

Surface quality represents a critical challenge in additive manufacturing (AM), with surface roughness serving as a key parameter that influences this aspect. In the aerospace industry, the surface roughness of the aviation components is a very important parameter. In this study, a typical Al alloy, AlSi10Mg, was selected to study its surface roughness when using Laser Powder Bed Fusion (LPBF). Two Random Forest (RF) models were established to predict the upper surface roughness of printed samples based on laser power, laser scanning speed, and hatch distance. Through the study, it is found that a two-dimensional (2D) RF model is successful in predicting surface roughness values based on experimental data. The best and minimum surface roughness is 2.98 μm, which is the minimum known without remelting. More than two-thirds of the samples had a surface roughness of less than 7.7 μm. The maximum surface roughness is 11.28 μm. And the coefficient of determination (R²) of the model was 0.9, also suggesting that the surface roughness of 3D-printed Al alloys can be predicted using ML approaches such as the RF model. This study helps to understand the relationship between printing parameters and surface roughness and helps print components with better surface quality.

1. Introduction

Additive manufacturing (AM), more commonly known as 3D printing, is a novel processing approach distinct from traditional manufacturing. Compared to traditional machining, its processing method is more flexible and rapid, and it can achieve rapid printing and manufacturing without mold, thereby garnering considerable favor within industries. AM has been extensively utilized in aerospace, medical, and other domains [1]. Some automotive engineers are also studying how to replace conventional cast metal parts and stamped parts with parts produced by AM, which can help reduce mold costs, reduce upfront trial production costs, improve material utilization, and shorten production cycles [2].

Compared to traditional manufacturing, AM also has certain disadvantages. For instance, compared to traditional machining, the precision of the parts produced by AM is lower, which not only affects the quality of the parts themselves but also the assembly of different parts, strength, sealing performance, etc. of the entire system. Some characteristics of AM processing, such as the need to add a support structure during processing, will also affect its surface accuracy. An important parameter for measuring accuracy is surface roughness. Surface roughness refers to the micro-geometric characteristics composed of small spacing and peaks and valleys on the machined surface. It is a micro-geometric error, also known as micro-unevenness. By using turning, grinding, and/or other processing methods, the surface roughness can be reduced to less than 0.01 µm [3]. The surface roughness of additively manufactured samples varies widely, ranging from 2 µm to 90 µm, which is mainly related to the process parameters used, the materials used, and the settings of the surface optimization parameters. In many kinds of additive manufacturing, Laser Powder Bed Fusion (L-PBF) has the lowest accuracy and the lowest surface roughness of the parts produced [4,5]. Gao et al. [6] have successfully reduced the surface roughness of Al-Si alloy parts printed by selective laser melting to 2 µm, which is the lowest known surface roughness of additively manufactured metal parts. Based on the results of their experiments, it was also noticed that the printing parameters are the most influential factors on the surface roughness of homogeneous metal parts.

To solve the specific relationship between the printing parameters and the surface roughness, artificial intelligence such as machine learning (ML) is preferred because too many variables are involved. ML is also capable of predicting based on obtained experimental results, where it represents the behavior of a computer that adapts its own computational aspects through experience gained from cyclic computing [7].

Several researchers have used ML models to predict the surface roughness of samples for AM. For instance, in order to predict the surface roughness of Ti-6Al-4V alloy samples printed by L-PBF, Fotovvati and Chou [8] studied the influence of various L-PBF process parameters on samples’ surface roughness; their results show that laser power has the greatest influence on the surface roughness of a sample. Li et al. [9] predicted the surface roughness of as-printed polylactic acid fabricated from fused deposition modeling. Yang et al. [10] developed an artificial neural network model to predict the surface roughness of printed 316L stainless steel samples in order to predict and improve the surface quality. They investigated the ensemble machine learning models to predict the mechanical properties of the 3D-printed Polylactic Acid (PLA) specimens. Deb et al. [11] used a variety of ML methods to predict the tensile strength and surface roughness of 3D-printed PLA based on process parameters. The experimental results show that the surface roughness of printed samples can be improved by adjusting the process parameters. Chen et al. [12] propose a machine learning method based on Gaussian process regression to construct a model between the Wire Arc Additive Manufacturing (WAAM) process parameters and top surface roughness. Experimental results demonstrate that the proposed method achieves less than 50 μm accuracy in surface roughness prediction. Gogulamudi et al. [13], to study the surface roughness of L-PBF aluminum alloy, developed a model to predict the optimal process parameters for producing AlSi10Mg components with desired surface roughness and Vickers microhardness.

Existing research covers a variety of approaches to ML and AM. This brings some inspiration to our research, but at the same time, there are several problems. For example, the vast majority of studies print a small number of experimental samples, in most cases fewer than 100 samples. Moreover, the surface roughness of the printed samples in most experiments is too large, which means that the printed parts may have surface defects and thus affect the surface roughness. This creates noisy labels in the data. These factors affect the predictions of ML models. Therefore, this experiment increased the number of experimental samples and reduced the surface defects of samples by controlling the range of process parameters to improve the accuracy and generality of ML predictions.

There are various types of ML models. In order to make it easy to give a suitable formula for predicting the process parameters’ effects on the surface roughness, Random Forest (RF) regression was selected to use in this study. RF is an integrated learning based on a decision tree algorithm. The decision trees approach is an important classification and regression method in data mining techniques [14], which is a predictive analytic model expressed in the form of binary and multinomial trees [15]. In the RF, each decision tree is independent and trained on a randomly selected subsample, which effectively reduces the risk of overfitting [16]. RF obtains the final regression results by averaging or weighted averaging the predictions of multiple decision trees [17]. Furthermore, according to the different number of feature values corresponding to each set of data, RF can be classified into different categories, such as one-dimensional (1D) RF regression models, two-dimensional (2D) RF regression, and so on. Descriptors are vectors used to depict the features of the data, which are mainly used to help ML models understand the data features [18]. A model with one descriptor for a piece of data is a 1D RF model, and a model with two descriptors for a piece of data is a 2D RF model.

To sum up, the aim of this study is to discover the relationship between surface roughness and process parameters for L-PBF. To achieve this, several groups of experimental samples were printed, a database was constructed, a RF model was established to predict the surface roughness of the printed samples according to the printing parameters, and the regression equations of both were given. The typical alloy selected in this experiment is AlSi10Mg, which is one of the most commonly used alloys in L-PBF. Its surface quality, however, is relatively poor, and its surface roughness is high [19], which is because Al alloys tend to have low fluidity [20], high thermal conductivity, and high laser reflectivity [21]. Improvement of its surface roughness can enhance its surface quality and can help avoid the necessity and cost of subsequent machining. Compared with the existing experiments, the parameter setting range in this study is more reasonable, and there are more experimental data. Machine learning has a larger database and a lower noise value of the data. The prediction results are more accurate and reasonable.

2. Experimental

2.1. Materials and Methods

The instrument used for printing was an FS273M printer (Farsoon Technologies, Changsha, China), and the surface roughness instrument used for the experiment was the Surftest SJ-310 measuring instrument (Mitutoyo, Suzhou, China). Each sample was measured three times, with each measurement taken at a distance of 0.8 μm. The three measurement lines and the edge of the sample were parallel to each other. Measurement lines 1 and 3 were 2 mm from the edge, respectively, and measurement line 2 was located in the center of the sample. In the process of measurement, some references were made to reduce measurement errors. [22,23] The surface profile of some samples was measured by the Countor GT K 3D profiler (Bruker, Berlin, Germany). Laser energy density, B, was used to describe the overall experimental parameters, as shown in the following formula (Equation (1)) [4]:

$$B={\displaystyle \frac{P}{vth}}$$

(1)

where P is the laser power (W), v is the scanning speed (mm/s), h is the hatch distance (µm), and t is the layer thickness (µm).

During the printing process, both too low and too high energy densities increase the surface roughness during printing. If the energy density is too low, it may lead to incomplete melting of the powder and make defects on the surface of the sample; if the energy density is too high, it may lead to splashing of the liquid metal and affect the surface roughness of the part [24,25]. The selected experimental variables were laser power, laser scanning speed, and hatch distance; see

Table 1. Printing parameters were used in this study.

Parameter	Basic Parameter	Range of Variable
Laser power	340 W	270~420 W
Laser scanning speed	1100 mm/s	800~1400 mm/s
Hatch distance	0.15 µm	0.08~0.16 µm

. The basic parameters were the commonly used AlSi10Mg printing parameters provided by the printer equipment manufacturer. On this basis, the research articles on AlSi10Mg should be referred to [26,27]. The range of parameter variation was given. In the experiment, the process parameters of sample 1 were set as the basic parameters, and the remaining sample parameters were determined by random selection. There was no replication of experimental data. Since the thickness of the powder layer cannot be adjusted during printing, we have standardized the powder layer thickness for all parts to 30 μm, as this is the most commonly used thickness for this aluminum alloy. For printing, the sample placement is shown in the following figure (Figure 1). A total of 144 different sets of experimental samples were designed. The samples were rectangles 1.2 cm in width by 1 cm in height. We conducted all sample prints at once, set all parts to the same scanning strategy, and eliminated the remelting process to minimize the influence of extraneous factors. Furthermore, the chosen printer was equipped with a dynamic focusing function that mitigates deviations in the laser incidence angle caused by varying positions of components on the substrate.

2.2. Random Forest Regression

As mentioned above, the RF regression is an algorithm based on bootstrap aggregation (bagging). Multiple decision trees are predicted in parallel, and the average predicted value of all decision trees is ultimately given [28]. The operation principle is also shown in Figure 2.

The RF model randomly extracts multiple samples from the original data set and generates multiple subsets of data. For each subset of data, a regression tree is constructed using the decision tree algorithm. When each node splits, some features are randomly selected, and the best features (laser power, laser scanning speed, and hatch distance) are selected for splitting. After all trees are trained, each decision tree is used to predict the newly input data points, and then all the predicted results are averaged to obtain the final predicted value. The equations for the RF model are as follows (Equation (2)) [29]:

$$y={\displaystyle \frac{1}{N}}{\sum }_{n=1}^N{y}_n$$

(2)

where $y$ is the average prediction result, $N$ is the number of decision trees, and $y_n$ is the prediction result given by n-numbered decision trees (1 < n < N). The specific process of each tree in the experiment is shown in Figure 3.

After the prediction result is obtained, the regression equation can be obtained by non-linear regression according to the split way of the decision tree. The regression method is the least squares method. The equation for the least squares method is expressed as follows (Equation (3)) [7]:

$$min{\sum }_{i=1}^{n}w{\left|y_i-\widehat{y_i}\right|}^2$$

(3)

where $y_{i }$ denotes the true observation, $\widehat{y_i}$ denotes the predicted value, $w$ denotes precision, and n denotes the number of decision trees.

In this experiment, there were 144 sets of data in total, where the eigenvalues were the printing parameters, and the three eigenvalues were the laser power, scanning speed, and scanning spacing. The target variable was surface roughness. For a better regression, a part of the data with a large noise value was removed, and the remaining data was set up as a database. The number of decision trees was set to 1000. The depth of each tree was set to 0. A 1D RF regression model and a 2D RF regression model were chosen to compare the regression equations and prediction accuracy given by the two models. The software used in this experiment was Anaconda (version 2.3.2). An RF model was built in Python (version 3.7.0).

The method of obtaining the regression equation was the standard equation method, which aims to obtain the parameter θ that minimizes the value of the cost function. The cost function formula was as follows:

To determine the prediction accuracy, some parameters, namely the mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and determination coefficient (R²), were used, and they are described below [11].

The formula for R² is as follows (Equation (4)):

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{\left(y_i-\widehat{y_i}\right)}^2}{{\sum }_{i=1}^n{\left(y_i-\overline{y}\right)}^2}}$$

(4)

where $y_i$ denotes the true observation, $\widehat{y_i}$ denotes the predicted value, $\overline{y}$ denotes the mean of the true observation, and n denotes the number of observations.

The formulas for MSE and RMSE are as follows (Equations (5) and (6)):

$$MSE={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{\left(y_i-\widehat{y_i}\right)}^2$$

(5)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{\left(y_i-\widehat{y_i}\right)}^2}$$

(6)

where $y_{i }$ denotes the true observation, $\widehat{y_i}$ denotes the predicted value, and n denotes the number of observations.

The equation for MAE is expressed as follows (Equation (7)):

$$MAE={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n\mid y_i-\widehat{y_i}\mid$$

(7)

where $y_{i }$ denotes the true observation, $\widehat{y_i}$ denotes the predicted value, and n denotes the number of observations.

3. Results

3.1. Experimental Result

The surface morphology and surface roughness of the printed parts were measured. The surface morphology of some parts was shown in Figure 4.

It can be seen from the surface profiles of some extracted samples that the surface profiles of the samples are relatively smooth, without major surface defects, and will not affect the measurement of surface roughness.

The printing parameters of the experimental samples were set in

Table 2. Process parameters of the samples (part).

Sample Number	Laser Power (W)	Laser Scanning Speed (mm/s)	Hatch Distance (µm)	Laser Energy Density (J/mm3)
1	340	1100	0.15	68.7
2	325	1251	0.08	108.2
3	321	1281	0.15	55.7
4	348	1091	0.14	75.9
5	343	1176	0.08	121.5
6	375	1330	0.08	117.5
7	399	917	0.11	131.9
8	398	912	0.16	90.9
9	317	810	0.13	100.3
10	292	882	0.12	92
11	411	938	0.09	162.3
12	330	1239	0.12	74
13	354	1050	0.15	74.9
14	360	927	0.12	107.9
15	330	887	0.08	155
16	366	1172	0.16	65.1
17	270	1128	0.12	66.5
18	288	869	0.12	92.1
19	343	1047	0.12	91
20	328	1382	0.1	79.1
…	…	…	…	…

. After printing, the surface roughness values of all samples were measured and organized into a histogram (Figure 5). From the histogram, it can be seen that the surface roughness values ranged from 2.90 µm to 11.30 µm. Most of the samples had surface roughness values clustered between 4.10 µm and 7.70 µm. We set the lower limit at 2.9 μm and the upper limit at 11.3 μm, dividing the range into seven equal intervals, each with a width of 1.2 μm. The printing parameters of the five best samples are organized in

Table 3. The best printing parameters and corresponding surface roughness (see Appendix Table A1 for the complete table).

Sample Number	Surface Roughness (µm)	Laser Power (W)	Laser Scanning Speed (mm/s)	Hatch Distance (µm)	Laser Energy Density (J/mm3)
14	3.26	360	927	0.12	107.9
26	3.95	395	1073	0.13	94.4
44	3.15	414	861	0.12	133.6
48	3.76	414	1079	0.09	142.1
116	2.98	415	917	0.1	150.9

, and the rest of the data are included in Appendix A.

Two points can be found in Table 3: Firstly, the energy density of several points with the lowest roughness is very high, e.g., ~130–150 J/mm³. Secondly, the best hatch distance is around 0.12 µm. This means that a combination of high laser power, low scanning speed, high laser energy density, and suitable hatch distance can reduce the surface roughness of the printed AlSi10Mg samples.

To further compare the relationship between surface roughness and laser energy density, the corresponding laser energy density and surface roughness of all 144 samples were counted and prepared as a scatter plot (Figure 6). The R² for this linear fit is 0.22. It can be seen from the figure that the laser energy density is indeed inversely proportional to the surface roughness as a whole, and the higher the laser energy density, the lower the surface roughness of the sample. The relationship between them is weakly and inversely correlated. However, the relationship between laser energy density and surface roughness is very complex, so this part is only a simple reasoning of the relationship between the two. The relationship between process parameters, laser energy density, and surface roughness also needs to be inferred from the ML prediction results.

Meanwhile, from the corresponding linear fitting, some data distribution is relatively discrete. This is most likely because of uncontrollable factors during the printing process. For example, the airflow field can impact the roughness of the printed parts [30]. The printer’s blower device can blow up fine spray powder during printing, which may splash onto other nearby sample surfaces, affecting surface forming and roughness. The surface roughness of individual samples fluctuates within a range of 1–2 μm, making predictions challenging when the surface roughness is excessively low. This leads to training data that is noisy, which affects the prediction results of the model [31]. To reduce errors in the regression prediction and improve the accuracy of the machine learning model, data that are too discrete are removed, and the remaining data are used as a database for the following ML regression.

3.2. Prediction Results and Regression Equations of the RF Regression Model (1D)

A 1D RF prediction model was run with a corresponding descriptor for each eigenvalue. The model is used to predict the training set and test set, respectively. The training set is used to estimate the parameters in the model so that the model reflects reality, while the test set is used to evaluate the predictive performance of the model. The comparison table between the predicted value and the real value is also sorted out, and part of the data are shown in

Table 4. Random Forest Regression (1D) prediction results (part).

Sample Number	Surface Roughness (µm)	Predicted Value (µm)	Error (%)	Descriptor
1	5.72	6.65	16%	3.45 × 10−3
2	6.95	7.86	13%	4.15 × 10−3
3	8.40	8.15	3%	4.31 × 10−3
4	6.00	6.35	6%	3.28 × 10−3
5	6.42	6.89	7%	3.59 × 10−3
6	5.44	6.51	20%	3.38 × 10−3
7	4.17	4.25	2%	2.09 × 10−3
8	4.78	4.25	11%	2.08 × 10−3
9	5.13	5.78	13%	2.96 × 10−3
10	6.62	7.23	9%	3.79 × 10−3
11	4.14	4.11	1%	2.01 × 10−3
12	6.63	7.62	15%	4.01 × 10−3
13	5.19	5.98	15%	3.07 × 10−3
14	3.26	5.20	60%	2.63 × 10−3
15	5.32	5.84	10%	3.00 × 10−3
16	7.01	6.17	12%	3.18 × 10−3
17	9.57	9.87	3%	5.30 × 10−3
18	7.61	7.31	4%	3.83 × 10−3
19	5.69	6.30	11%	3.25 × 10−3
20	8.18	8.28	1%	4.38 × 10−3
…	…	…	…	…

.

In the regression, the first 100 sets of data are used as the test set, and the last 20 sets of data are used as the training set. The data, including the real values and predicted values, as well as the corresponding eigenvalue of each data, are included in Appendix

Table A2. Random Forest Regression(1D) prediction results. Note: groups 1–100 are the training set data, and groups 101–120 are the test set data.

Sample Number	Surface Roughness (µm)	Predicted Value (µm)	Error (%)	Descriptor
1	5.72	6.65	16%	3.45 × 10−3
2	6.95	7.86	13%	4.15 × 10−3
3	8.40	8.15	3%	4.31 × 10−3
4	6.00	6.35	6%	3.28 × 10−3
5	6.42	6.89	7%	3.59 × 10−3
6	5.44	6.51	20%	3.38 × 10−3
7	4.17	4.25	2%	2.09 × 10−3
8	4.78	4.25	11%	2.08 × 10−3
9	5.13	5.78	13%	2.96 × 10−3
10	6.62	7.23	9%	3.79 × 10−3
11	4.14	4.11	1%	2.01 × 10−3
12	6.63	7.62	15%	4.01 × 10−3
13	5.19	5.98	15%	3.07 × 10−3
14	7.01	6.17	60%	3.18 × 10−3
15	9.57	9.87	10%	5.30 × 10−3
16	7.61	7.31	12%	3.83 × 10−3
17	5.69	6.30	3%	3.25 × 10−3
18	8.18	8.28	4%	4.38 × 10−3
19	5.33	5.66	11%	2.89 × 10−3
20	5.36	5.47	1%	2.78 × 10−3
21	4.92	6.00	6%	3.08 × 10−3
22	4.84	5.85	2%	3.00 × 10−3
23	6.49	5.91	22%	3.03 × 10−3
24	5.13	4.96	21%	2.49 × 10−3
25	4.41	5.05	9%	2.54 × 10−3
26	7.14	7.79	27%	4.11 × 10−3
27	7.24	7.70	3%	4.06 × 10−3
28	8.13	8.63	14%	4.59 × 10−3
29	4.92	5.81	9%	2.97 × 10−3
30	4.23	4.82	6%	2.41 × 10−3
31	6.71	7.84	6%	4.14 × 10−3
32	5.20	5.21	18%	2.63 × 10−3
33	6.71	6.63	14%	3.44 × 10−3
34	4.70	4.45	17%	2.20 × 10−3
35	11.28	10.14	0%	5.45 × 10−3
36	6.80	7.21	1%	3.78 × 10−3
37	4.91	5.82	5%	2.98 × 10−3
38	4.88	5.59	10%	2.85 × 10−3
39	5.03	5.80	6%	2.97 × 10−3
40	3.15	3.69	19%	1.77 × 10−3
41	7.67	7.75	22%	4.09 × 10−3
42	6.60	7.41	14%	3.89 × 10−3
43	9.31	9.61	15%	5.15 × 10−3
44	3.76	4.65	17%	2.31 × 10−3
45	5.50	5.17	1%	2.61 × 10−3
46	6.09	6.44	12%	3.34 × 10−3
47	8.28	7.04	3%	3.68 × 10−3
48	5.36	6.25	24%	3.23 × 10−3
49	4.84	5.81	6%	2.98 × 10−3
50	10.81	9.27	6%	4.95 × 10−3
51	4.64	4.95	15%	2.49 × 10−3
52	5.72	6.06	17%	3.12 × 10−3
53	5.01	5.61	20%	2.86 × 10−3
54	4.23	3.96	14%	1.92 × 10−3
55	4.23	3.93	7%	1.90 × 10−3
56	8.92	9.71	6%	5.20 × 10−3
57	5.65	6.71	12%	3.49 × 10−3
58	7.20	7.57	6%	3.98 × 10−3
59	5.26	5.29	7%	2.68 × 10−3
60	5.14	6.12	26%	3.15 × 10−3
61	8.24	7.99	9%	4.22 × 10−3
62	6.67	7.04	19%	3.68 × 10−3
63	3.65	4.74	5%	2.37 × 10−3
64	5.64	6.57	1%	3.41 × 10−3
65	8.22	7.96	19%	4.20 × 10−3
66	10.42	9.30	3%	4.97 × 10−3
67	7.77	7.38	6%	3.87 × 10−3
68	4.71	4.86	30%	2.43 × 10−3
69	7.54	6.79	17%	3.54 × 10−3
70	6.42	5.69	3%	2.91 × 10−3
71	5.47	5.84	11%	2.99 × 10−3
72	4.90	5.82	5%	2.98 × 10−3
73	5.81	5.75	3%	2.94 × 10−3
74	5.48	6.43	10%	3.33 × 10−3
75	7.64	7.20	11%	3.77 × 10−3
76	7.14	7.73	7%	4.07 × 10−3
77	5.34	6.58	19%	3.42 × 10−3
78	4.91	6.02	1%	3.10 × 10−3
79	4.94	4.90	17%	2.46 × 10−3
80	8.37	6.06	6%	3.12 × 10−3
81	9.46	8.71	8%	4.63 × 10−3
82	7.10	5.56	23%	2.83 × 10−3
83	7.51	6.71	23%	3.49 × 10−3
84	7.70	7.73	1%	4.07 × 10−3
85	9.92	10.02	8%	5.38 × 10−3
86	4.37	5.62	11%	2.87 × 10−3
87	9.59	9.94	0%	5.34 × 10−3
88	4.06	3.86	1%	1.86 × 10−3
89	8.98	7.78	29%	4.10 × 10−3
90	9.88	9.76	4%	5.23 × 10−3
91	7.84	6.54	5%	3.39 × 10−3
92	6.47	5.72	0%	2.93 × 10−3
93	8.15	8.79	13%	4.68 × 10−3
94	7.11	8.01	1%	4.23 × 10−3
95	6.54	6.77	12%	3.52 × 10−3
96	5.51	5.84	8%	3.00 × 10−3
97	7.36	7.19	13%	3.77 × 10−3
98	5.37	5.73	4%	2.93 × 10−3
99	4.70	5.06	6%	2.55 × 10−3
100	4.77	4.87	2%	2.44 × 10−3
101	8.11	7.04	9%	3.68 × 10−3
102	7.38	5.80	7%	2.97 × 10−3
103	7.31	8.75	8%	4.66 × 10−3
104	6.77	7.93	2%	4.19 × 10−3
105	6.84	6.80	16%	3.54 × 10−3
106	10.01	9.21	1%	4.92 × 10−3
107	10.18	8.65	15%	4.60 × 10−3
108	7.40	6.39	8%	3.31 × 10−3
109	6.45	7.29	10%	3.82 × 10−3
110	6.00	5.50	13%	2.80 × 10−3
111	5.43	5.26	8%	2.66 × 10−3
112	10.57	10.61	3%	5.71 × 10−3
113	7.33	6.71	0%	3.49 × 10−3
114	3.67	3.57	10%	1.70 × 10−3
115	6.11	6.26	8%	3.23 × 10−3
116	6.21	6.05	3%	3.11 × 10−3
117	7.06	5.81	2%	2.98 × 10−3
118	7.92	5.55	3%	2.83 × 10−3
119	5.98	5.58	7%	2.85 × 10−3
120	7.96	8.06	1%	4.26 × 10−3

The predicted and true values given by the model were sorted into graphs for the training set and the test set, respectively (Figure 7).

The formula for the regressed surface roughness, R, is as follows (Equation (8)):

$$R=\ln \left({\displaystyle \frac{1752.6a}{b^2}}\right)+0.6$$

(8)

where a is the laser scanning speed (mm/s), and b is the laser power (W). The image of the equation is shown in Figure 8. According to the established equation, the surface roughness is proportional to laser scanning speed and inversely proportional to laser power, suggesting that the higher the laser power, the lower the scanning speed, the lower the surface roughness, and the better the surface performance of the printed sample. This is consistent with previous experimental findings that surface roughness is inversely proportional to laser energy density.

The regression equation does not contain all the features, which indicates that there are some problems in the pruning process of the decision tree, resulting in a lack of features. To solve this phenomenon, it is necessary to add data descriptors so that the RF model can understand the data more accurately and make the model more complex to avoid the influence of single decision tree pruning errors.

3.3. Prediction Results and Regression Equations of Random Forest Regression Model (2D)

Table 5. Random Forest Regression (2D) prediction results (part).

Sample Number	Surface Roughness (µm)	Predicted Value (µm)	Error (%)	Descriptor 1	Descriptor 2
1	5.72	6.25	9%	2.14 × 101	−3.76 × 102
2	6.95	7.80	12%	2.06 × 101	−2.09 × 102
3	8.40	7.88	6%	2.12 × 101	−3.92 × 102
4	6.00	5.91	1%	2.14 × 101	−3.66 × 102
5	6.42	6.73	5%	2.08 × 101	−2.18 × 102
6	5.44	6.29	16%	2.12 × 101	−3.05 × 102
7	4.17	3.81	9%	2.17 × 101	−3.48 × 102
8	4.78	4.53	5%	2.21 × 101	−4.99 × 102
9	5.13	5.60	9%	2.10 × 101	−2.10 × 102
10	6.62	7.50	8%	2.06 × 101	−1.86 × 102
11	4.14	3.82	8%	2.17 × 101	−3.23 × 102
12	6.63	7.17	8%	2.11 × 101	−3.19 × 102
13	5.19	5.60	20%	2.16 × 101	−3.92 × 102
14	7.01	6.57	6%	2.18 × 101	−5.05 × 102
15	9.56	9.84	3%	2.03 × 101	−2.14 × 102
16	7.60	7.70	1%	2.05 × 101	−1.79 × 102
17	5.69	5.75	1%	2.12 × 101	−2.92 × 102
18	8.17	7.88	4%	2.09 × 101	−2.94 × 102
19	5.33	5.33	0%	2.12 × 101	−2.61 × 102
20	5.359	5.55	4%	2.18 × 101	−4.64 × 102
…	…	…	…	…	…

compares some of the experimental and predicted values in the 2D RF model. The complete data of the samples, as well as the eigenvalues corresponding to each data point, are listed in Appendix

Table A3. Random Forest Regression(2D) prediction results. Note: groups 1–100 are the training set data, and groups 101–120 are the test set data.

Sample Number	Surface Roughness (µm)	Predicted Value (µm)	Error (%)	Descriptor 1	Descriptor 2
1	5.72	6.25	9%	2.14 × 101	−3.76 × 102
2	6.95	7.80	12%	2.06 × 101	−2.09 × 102
3	8.40	7.88	6%	2.12 × 101	−3.92 × 102
4	6.00	5.91	1%	2.14 × 101	−3.66 × 102
5	6.42	6.73	5%	2.08 × 101	−2.18 × 102
6	5.44	6.29	16%	2.12 × 101	−3.05 × 102
7	4.17	3.81	9%	2.17 × 101	−3.48 × 102
8	4.78	4.53	5%	2.21 × 101	−4.99 × 102
9	5.13	5.60	9%	2.10 × 101	−2.10 × 102
10	6.62	7.50	8%	2.06 × 101	−1.86 × 102
11	4.14	3.82	8%	2.17 × 101	−3.23 × 102
12	6.63	7.17	8%	2.11 × 101	−3.19 × 102
13	5.19	5.60	20%	2.16 × 101	−3.92 × 102
14	7.01	6.58	6%	2.18 × 101	−5.05 × 102
15	9.57	9.84	3%	2.03 × 101	−2.14 × 102
16	7.61	7.70	1%	2.05 × 101	−1.79 × 102
17	5.69	5.75	1%	2.12 × 101	−2.92 × 102
18	8.18	7.88	4%	2.09 × 101	−2.94 × 102
19	5.33	5.33	0%	2.12 × 101	−2.61 × 102
20	5.36	5.55	4%	2.18 × 101	−4.64 × 102
21	4.92	5.45	11%	2.13 × 101	−3.11 × 102
22	4.84	5.30	10%	2.14 × 101	−3.17 × 102
23	6.49	6.42	1%	2.18 × 101	−5.16 × 102
24	5.13	5.78	13%	2.19 × 101	−5.11 × 102
25	4.41	4.45	1%	2.13 × 101	−2.54 × 102
26	7.14	8.14	14%	2.04 × 101	−1.73 × 102
27	7.24	7.35	2%	2.08 × 101	−2.59 × 102
28	8.13	9.02	11%	2.03 × 101	−1.84 × 102
29	4.92	6.04	23%	2.08 × 101	−1.72 × 102
30	4.23	4.64	10%	2.19 × 101	−4.34 × 102
31	6.71	7.59	13%	2.07 × 101	−2.36 × 102
32	5.20	4.76	8%	2.13 × 101	−2.66 × 102
33	6.71	6.52	3%	2.08 × 101	−2.05 × 102
34	4.70	4.27	9%	2.12 × 101	−1.94 × 102
35	11.28	10.32	9%	2.01 × 101	−1.85 × 102
36	6.80	6.89	1%	2.13 × 101	−3.82 × 102
37	4.91	5.52	13%	2.14 × 101	−3.20 × 102
38	4.88	5.29	8%	2.11 × 101	−2.35 × 102
39	5.03	5.54	10%	2.11 × 101	−2.28 × 102
40	3.15	3.54	12%	2.20 × 101	−4.06 × 102
41	7.67	7.49	2%	2.13 × 101	−3.94 × 102
42	6.60	7.17	9%	2.08 × 101	−2.42 × 102
43	9.31	9.78	5%	2.02 × 101	−1.89 × 102
44	3.76	4.75	26%	2.17 × 101	−3.82 × 102
45	5.50	5.69	3%	2.20 × 101	−5.20 × 102
46	6.09	6.18	2%	2.10 × 101	−2.35 × 102
47	8.28	7.97	4%	2.04 × 101	−1.50 × 102
48	5.36	5.77	8%	2.13 × 101	−3.11 × 102
49	4.84	5.58	15%	2.16 × 101	−3.89 × 102
50	10.81	10.36	4%	1.99 × 101	−1.39 × 102
51	4.64	4.87	5%	2.11 × 101	−1.89 × 102
52	5.72	6.00	5%	2.13 × 101	−3.38 × 102
53	5.01	5.12	2%	2.15 × 101	−3.42 × 102
54	4.23	4.64	10%	2.22 × 101	−5.39 × 102
55	4.23	3.30	22%	2.17 × 101	−3.11 × 102
56	8.92	9.38	5%	2.05 × 101	−2.52 × 102
57	5.65	6.75	19%	2.08 × 101	−2.11 × 102
58	7.20	7.31	1%	2.12 × 101	−3.75 × 102
59	5.26	5.74	9%	2.17 × 101	−4.25 × 102
60	5.14	5.98	16%	2.09 × 101	−2.03 × 102
61	8.24	7.55	8%	2.09 × 101	−2.99 × 102
62	6.67	6.66	0%	2.13 × 101	−3.69 × 102
63	3.65	4.34	19%	2.17 × 101	−3.51 × 102
64	5.64	6.39	13%	2.15 × 101	−4.12 × 102
65	8.22	7.55	8%	2.11 × 101	−3.36 × 102
66	10.42	9.33	10%	2.03 × 101	−2.09 × 102
67	7.77	8.15	5%	2.04 × 101	−1.49 × 102
68	4.71	4.29	9%	2.17 × 101	−3.62 × 102
69	7.54	7.55	0%	2.05 × 101	−1.49 × 102
70	6.42	6.51	1%	2.06 × 101	−1.40 × 102
71	5.47	5.24	4%	2.15 × 101	−3.33 × 102
72	4.90	6.00	23%	2.16 × 101	−4.17 × 102
73	5.81	6.83	18%	2.05 × 101	−1.30 × 102
74	5.48	6.12	12%	2.10 × 101	−2.29 × 102
75	7.64	7.04	8%	2.08 × 101	−2.21 × 102
76	7.14	7.56	6%	2.13 × 101	−4.13 × 102
77	5.34	6.22	16%	2.10 × 101	−2.56 × 102
78	4.91	5.49	12%	2.13 × 101	−2.86 × 102
79	4.94	4.28	13%	2.16 × 101	−3.16 × 102
80	8.37	7.75	7%	2.19 × 101	−6.04 × 102
81	9.46	9.19	3%	2.03 × 101	−1.75 × 102
82	7.10	6.72	5%	2.20 × 101	−5.74 × 102
83	7.51	6.49	14%	2.12 × 101	−3.36 × 102
84	7.70	7.46	3%	2.08 × 101	−2.57 × 102
85	9.92	9.64	3%	2.05 × 101	−2.81 × 102
86	4.37	5.46	25%	2.10 × 101	−2.01 × 102
87	9.59	9.74	1%	2.04 × 101	−2.38 × 102
88	4.06	3.64	10%	2.19 × 101	−3.82 × 102
89	8.98	8.96	0%	2.02 × 101	−1.34 × 102
90	9.88	10.11	2%	2.01 × 101	−1.76 × 102
91	7.84	7.52	4%	2.04 × 101	−1.43 × 102
92	6.47	6.97	8%	2.19 × 101	−5.53 × 102
93	8.15	8.77	8%	2.05 × 101	−2.18 × 102
94	7.11	7.97	12%	2.06 × 101	−2.09 × 102
95	6.54	6.28	4%	2.11 × 101	−2.75 × 102
96	5.51	5.54	1%	2.11 × 101	−2.42 × 102
97	7.36	6.69	9%	2.11 × 101	−3.15 × 102
98	5.37	5.43	1%	2.11 × 101	−2.19 × 102
99	4.70	4.44	6%	2.14 × 101	−2.60 × 102
100	4.77	4.55	5%	2.16 × 101	−3.45 × 102
101	8.11	7.02	8%	2.07 × 101	−2.01 × 102
102	7.38	7.02	5%	2.18 × 101	−5.38 × 102
103	7.31	8.34	14%	2.09 × 101	−3.32 × 102
104	6.77	7.49	11%	2.10 × 101	−3.14 × 102
105	6.84	6.59	4%	2.13 × 101	−3.60 × 102
106	10.01	9.45	6%	2.02 × 101	−1.84 × 102
107	10.18	9.44	7%	2.01 × 101	−1.53 × 102
108	7.40	7.96	8%	2.03 × 101	−1.18 × 102
109	6.45	6.91	7%	2.09 × 101	−2.52 × 102
110	6.00	5.64	6%	2.17 × 101	−4.27 × 102
111	5.43	5.75	6%	2.17 × 101	−4.50 × 102
112	10.57	10.35	2%	2.02 × 101	−2.30 × 102
113	7.33	6.97	5%	2.15 × 101	−4.43 × 102
114	3.67	3.98	8%	2.23 × 101	−5.12 × 102
115	6.11	6.04	1%	2.12 × 101	−3.05 × 102
116	6.21	5.77	7%	2.12 × 101	−2.87 × 102
117	7.06	7.15	1%	2.18 × 101	−5.34 × 102
118	7.92	7.08	11%	2.19 × 101	−5.77 × 102
119	5.98	5.53	8%	2.14 × 101	−3.38 × 102
120	7.96	7.67	4%	2.11 × 101	−3.39 × 102

.

Furthermore, the predicted values and experimental values given by the model on the training set and the test set were organized into line plots and scatter plots, respectively, see Figure 9.

The regressed surface roughness, R, using the 2D RF model is as follows (Equation (9)):

$$R=-5.786\ln \left({\displaystyle \frac{b^4}{c}}\right)+{\displaystyle \frac{0.0187ac}{\sin \left(\ln b\right)}}+141.138$$

(9)

where a is the laser scanning speed (mm/s), b is the laser power (W), and c is the hatch distance (µm). It can be seen that the regression equation given by the 2D RF regression model is different from that of the 1D model. Since there are three variables in this regression equation, it is not possible to draw the function diagram directly. After setting the hatch distance to 0.01 µm, the function diagram is presented in Figure 10.

By checking the regression equation, it can be found that the value of $\sin \left(\ln b\right)$ in the equation has a small change (0.097–0.105) in the laser power range (270 W–420 W) given in this experiment, which can be regarded as a constant. Based on this, the surface roughness of the printed samples shows a tendency of decreasing with the increase in laser power and increasing with the increase in laser scanning speed, while the relationship between the surface roughness and the hatch distance depends on the specific parameters.

4. Discussion

By comparing the prediction accuracy of the two different models, the reference coefficients for the 1D and 2D RF models are sorted in

Table 6. Comparison of evaluation parameters between the 1D model and 2D model.

Evaluation Parameter	R2	MSE	RMSE	MAE
Argument (1D model)	0.865	0.350	0.592	0.582
Argument (2D model)	0.907	0.255	0.505	0.464

. From the table, it can be seen that, in comparison, the 2D RF regression model has lower values of MSE, RMSE, and MAE, and its R² is closer to 1. All four evaluation parameters are better than the 1D RF regression model, indicating that the 2D RF regression model gives a more accurate prediction.

Based on the regression equations obtained above, it was found that the two equations have similar resulting images and patterns of change, but the regression equation given by the 2D RF regression model includes the variable of hatch distance. This is because by adding a descriptor, the ML process learns more features, which helps understand the relationship between the input features and the real observations. A more reasonable regression equation is therefore realized by the 2D RF regression; also, the regression equation given by the 2D RF regression model contains all the eigenvalue variables. Based on the 2D RF regression equation, it can be observed that surface roughness decreases as laser power increases and increases as scanning speed increases. Additionally, the relationship between surface roughness and hatch distance varies based on the specific value of the hatch distance. Similar patterns can also be derived from the 1D RF regression equation. As laser power increases, scanning speed decreases, leading to an increase in laser energy density and a decrease in surface roughness. The conclusion aligns with our findings at the end of Chapter 3.1. However, it is important to note that this conclusion may not hold true when the process parameters fall outside the range specified in this experiment. Additionally, the surface roughness could be impacted by uncontrollable external factors, leading to a small margin of error. By further comparing the results of this study with previous studies (

Table 7. Surface roughness results obtained in this study and other references [4,23].

	Reference Study	Our Study
Minimum surface roughness	2.5 μm [6] 8.67 μm [13]	2.95 μm
Machine learning model	Deep learning [13]	Random forest
Regression equation	Excluded	Contained

), it is evident that our results are among the best ones, achieving a minimum surface roughness of below 3 μm [6,13]. The experimental results show that surface defects have less impact, leading to more accurate predictions. Additionally, the machine learning database used in this study is larger, allowing for a wider range of predictions. This experiment also obtained regression equations for AlSi10Mg surface roughness and process parameters, a first in known research. This contributes to a better understanding of the relationship between surface roughness and process parameters.

5. Conclusions and Outlook

5.1. Conclusions

The main results obtained in this study are summarized as follows:

(1)

In order to study the correlation between the surface roughness of a typical Al alloy and the printing parameters, experiments were designed in which a total of 144 sets of samples were printed to study changes in surface roughness under the influence of key printing parameters. The lowest surface roughness achieved was 2.95 μm, indicating that it is possible to print Al alloys with a good surface quality by process optimization without using remelting.

(2)

Based on the obtained experimental data, Random Forest regression was built to regress and predict the results. After optimizing the model, a 2D prediction model was developed with high prediction accuracy. The R² of the model is 0.907, with an MSE of 0.255, RMSE of 0.505, and MAE of 0.464. The specific relationship equation between the key printing parameters and surface roughness was also derived. A 2D RF model can maintain high prediction accuracy on both the training set and test set. The experimental parameters in the training set and test set cover the range of printing parameters of AlSi10Mg. This proves that the obtained ML model can provide accurate prediction results for the indicated roughness study of the aluminum alloy.

5.2. Outlook

In comparison to existing experimental results, this experiment collected a larger amount of data, with a total of 144 groups of experimental data being designed. The surface roughness of the samples was also lower. The experiment used the common printing parameter interval for AlSi10Mg. The average prediction error was less than 0.5 μm, indicating higher prediction accuracy across a wider range of applications. The regression equation between process parameters and surface roughness was also proposed in this experiment, which helps us to understand the relationship between the two. However, there are some drawbacks to this experiment. Even though the data set used for machine learning in this experiment was already much larger than the data set in the existing research results, to predict the results more accurately, it is still necessary to build a data set containing more experimental data. If a data set of more than a thousand printed parts can be included, then the prediction accuracy of the model will surpass all known results.