Machine Learning-Enabled Prognostication of Tensile Strength in 316L Stainless Steel Through Additive Manufacturing Processes

Abstract

The tensile strength of components fabricated through additive manufacturing processes is of paramount importance for their implementation in practical engineering applications. However, the intricacy of the process parameters renders the prediction of tensile strength a formidable challenge. In this scholarly work, a predictive model for the tensile strength of 316L stainless steel components produced via SLM was developed through the synergistic integration of CNN and RF. The model was trained on a dataset comprising 42 datasets and subsequently validated against 12 sets of experimental data. The model’s predictive performance was quantified using MSE and MAE, which were recorded as 0.00295 and 0.0344, respectively. These values represent a reduction of 3.28% and 31.88% when compared to the predictive accuracy achieved by employing CNN in isolation. Furthermore, the correlation coefficient achieved a substantial increase of 74.18%, reaching a value of 0.9576, which is indicative of a high degree of accuracy in the model’s predictive outcomes. With the same sample size, the incorporation of relative density and Vickers hardness as additional input conditions resulted in a reduction in prediction accuracy. The tensile strength prediction model presented herein demonstrates the capability for high-precision prediction even with small datasets, thereby offering a theoretical framework that may guide future endeavors in the prediction of mechanical properties for a broader spectrum of materials.

1. Introduction

Selective laser melting (SLM), an esteemed subset of additive manufacturing (AM) technology, is distinguished by its rapid prototyping capabilities, exceptional precision, elevated material efficiency, and the capacity for monolithic part fabrication [1,2]. In the contemporary era, SLM has emerged as a transformative force in the realms of aerospace, automotive engineering, die and mold production, hydraulic component manufacturing, and medical device development [3,4,5,6,7]. The tensile strength, a pivotal mechanical attribute of components crafted via SLM, exerts a profound influence on their applicability across these diverse sectors. Consequently, the enhancement of tensile strength in SLM-fabricated parts has consistently been a subject of rigorous investigation and pursuit among the scholarly community.

Laser power, scanning speed, hatch spacing, and layer thickness constitute the quartet of process parameters that significantly dictate the mechanical properties of metallic components fabricated through SLM [8,9,10,11]. Hyer et al. discerned that laser power levels that are either excessively high or insufficient can precipitate porosity defects or incomplete metal melting, respectively, both of which can adversely affect the mechanical properties of the resultant parts [12]. Martin et al. observed that the tensile strength of SLM-formed components tends to exhibit an initial increase followed by a subsequent decrease with variations in scanning speed [13]. Elsayed et al. determined that diminishing the hatch spacing within an optimal range can facilitate more effective melting of metal powder, thereby augmenting the mechanical properties of the formed parts [14]. Ali et al. concluded that augmenting the powder layer thickness can mitigate the residual stress generated during the printing process, yet this may concurrently compromise the mechanical integrity of the components [15]. The influence of the aforementioned process parameters on the mechanical properties is traditionally ascertained through empirical experimentation, a process that is inherently time-consuming and labor-intensive. Consequently, there exists an imperative requirement to develop a predictive methodology for the mechanical properties of SLM-formed parts. Such a method would enable swift and efficient control over the mechanical properties, thereby streamlining the manufacturing process and enhancing the quality assurance of SLM-produced components.

In the contemporary epoch, technological advancements related to computing have progressed at an exponential rate, with machine learning emerging as a cornerstone in the scientific and technological domains. It has been instrumental in propelling the evolution of automation, intelligent systems, and data-informed decision-making processes. Its infiltration into the realm of materials science has likewise become increasingly pervasive [16,17,18,19]. Machine learning, through the analysis of extensive datasets and the extraction of underlying patterns, is capable of accomplishing a spectrum of tasks. These include the prognostication of material mechanical properties [20], the optimization of process parameters [21], the selection of material compositions [22], and the refinement of material formulations [23]. Barrionuevo et al. employed a suite of seven machine learning algorithms to predict the relative density of SLM-formed parts, revealing that the Gradient Boosting Regressor exhibited the highest predictive accuracy, succeeded by the multilayer perceptron and the random forest regressor [24]. Lu et al. leveraged a dataset encompassing SLM process parameters and relative density from extant literature, constructed a backpropagation neural network (BPNN) model and its variants: genetic algorithm-optimized BPNN and adaptive genetic algorithm optimization models [25]. The predictive accuracies of these models were recorded at 73.5%, 75.3%, and 79.9%, respectively. Yadav et al. trained and optimized the tensile strength of fused deposition modeling (FDM) specimens utilizing an artificial neural network (ANN) and a genetic algorithm–artificial neural network (GA-ANN) hybrid approach [26]. The findings demonstrated that the GA-ANN enhanced the tensile strength by 4.54%. Huang et al. developed a predictive model for the creep rupture life of superalloys, employing a dimensionality reduction strategy informed by physical metallurgical models and phase diagram calculations [27]. The model was validated across three alloys, with the relative error between predicted and experimental values remaining below 10%. From the aforementioned research endeavors, it is evident that the construction of predictive models via machine learning can effectively fulfill the objective of material property prediction. However, when confronted with a diminutive dataset and a dearth of data for machine learning, achieving high-precision predictions is often a challenging endeavor.

In the process of practical engineering, due to the high cost of materials and equipment usage, the long time required to obtain a large amount of data, and the scarcity of data under special conditions, it is sometimes impossible to collect a large amount of data. This requires researchers to use small datasets for rapid prediction and decision-making. Moreover, processing large-scale datasets requires powerful computing resources, including high-performance computers and a large amount of storage space. Small datasets can effectively achieve the goals of artificial intelligence training and solve the above-mentioned problems [28,29,30]. By reducing the complexity of data collection and processing, they lower the demand for computational resources and storage space. Meanwhile, through techniques such as transfer learning and regularization, small datasets can quickly train models with good generalization capabilities under limited resources. This approach avoids the high costs and long-term investments associated with large-scale data training and is particularly suitable for scenarios with limited resources.

In the present scholarly work, a machine learning dataset comprising 42 datasets was meticulously established; the process parameters of SLM served as the input parameters, including laser power, scanning speed, hatch spacing, and powder layer thickness. To explore a broader range of predictive capabilities, relative density and Vickers hardness were also included as performance metrics. Additionally, the tensile strength of SLM-formed 316L stainless steel was the dependent variable. A predictive model for the tensile strength of SLM-formed 316L stainless steel was constructed utilizing a convolutional neural network (CNN) in conjunction with a random forest (RF) algorithm. The efficacy of this model was substantiated through 12 predictive experiments. The findings of this investigation offer a novel methodology for prognostically estimating the mechanical strength of components fabricated via the technologically sophisticated SLM process.

2. Materials and Methods

2.1. Experimental Materials and Specimen Preparation

In the current research, 316L stainless steel powder, manufactured by Zhongyuan Advanced Materials Co., Ltd. (Ningbo, China), was employed for SLM fabrication, with its chemical composition detailed in

Table 1. Chemical composition of 316L powder (ω/%).

Element	C	S	P	Cr	Si	Mn	Mo	Ni	Fe
Content	≤0.03	≤0.03	≤0.045	16~18	≤1	≤2	2~3	10~14	Bal.

. The particle size distribution of the powder spanned from 15 to 53 μm, characterized by D10 = 19.77 μm, D50 = 33.84 μm, and D90 = 55.42 μm. The Hall flow rate was recorded at 17.80 s per 50 g, the loose bulk density was measured at 4.19 g per cm³, and the tapped density was ascertained to be 4.78 g per cm³. These parameters collectively indicate a favorable flowability of the powder during the SLM forming process.

The specimens were fabricated utilizing the M280 apparatus, manufactured by SLM Solutions (Lübeck, Germany). Tensile specimens were dog-bone-shaped, while specimens for relative density and Vickers hardness testing were cubes measuring 10 × 10 × 10 mm³. This state-of-the-art equipment is equipped with an IPG fiber laser, boasting a maximum laser power output of 400 watts, and uses a single laser for printing. The diameter of the laser spot is 71 μm. Prior to the commencement of the printing process, an ultra-high purity argon gas with a purity level of 99.999% was purged into the forming chamber. This procedural step is imperative to maintain the oxygen content below 1000 parts per million (ppm) throughout the fabrication process, thereby mitigating the risk of oxidation. The substrate, fashioned from the identical 316L material as the tensile specimens, was preheated to a temperature of 100 degrees Celsius to alleviate thermal stress during the SLM process. The process parameters of SLM have a significant impact on the mechanical properties of the formed specimens. Therefore, the process parameters for tensile specimens were formulated within a reasonable range, as shown in

Table 2. SLM forming process parameters for tensile specimens.

Process Parameters	Values
Laser power/W	100, 200, 300
Scanning speed/mm·s−1	600, 800, 1000
Hatch spacing/mm	0.1, 0.12, 0.14
Layer thickness/μm	30, 50

. In this study, an orthogonal experimental design was conducted based on the SLM processing parameters listed in Table 2, and 42 samples were selected as the training set and 12 samples as the test set. Within each set, samples were trained and predicted using random sampling to ensure that the model maintains good generalization ability and robustness across different parameter combinations. A visual representation of the macroscopic appearance of the fabricated specimens is depicted in Figure 1.

2.2. Relative Density, Vickers Hardness, and Tensile Test

Relative density was measured by metallographic methods. The cubic specimens were successively ground with 400#, 800#, 1500#, 2000#, 3000#, and 5000# sandpapers and then polished to a mirror finish with 0.05 μm colloidal silica. The image acquisition was performed under a laser scanning confocal microscope, and the relative density was calculated using Image J (1.8.0) software.

Vickers hardness was measured with a Vickers hardness tester equipped with a diamond indenter, manufactured by Taiming Optical Instrument Co., Ltd. (Shanghai, China). A load of 300 gf was applied and held for 15 s; the instrument’s software (MH VK 1.4.2) then calculated the Vickers hardness value from the indentation area.

Tensile testing of the specimens was executed employing the CTM 5305 electronic universal testing machine, a product of MTS Systems Co., Ltd. (Shenzhen, China). Throughout the tensile procedure, the upper clamp is utilized to secure the specimen, thereby nullifying the force exerted by the machine at this juncture. Subsequently, the lower clamp is engaged to grasp the specimen, and the zero button is activated to compensate for any tensile or compressive forces induced during the clamping phase. Tensile tests were performed three times for each specimen, with the results being averaged. The tensile speed was set at 1 mm/min. The fracture of the specimens essentially occurred within the gauge length, as shown in Figure 2. Data from specimens that fractured outside the gauge length were not used; instead, substitute specimens were tested again.

2.3. Machine Learning Algorithms

CNNs are renowned for their adeptness in harnessing convolutional layers to autonomously distill spatial features from input datasets. Subsequently, these networks diminish the spatial dimensions of the data through the application of pooling layers, culminating in the execution of classification or regression tasks by means of fully connected layers. CNNs excel in capturing localized features and incrementally constructing more intricate and abstract feature representations in a hierarchical manner.

RF represents an ensemble learning paradigm predicated on the foundation of decision trees. This method enhances the precision and robustness of predictive models by simultaneously constructing a multitude of decision trees and amalgamating their individual predictions. Each constituent decision tree is trained on a distinct subset of the data, with an element of randomness introduced during the feature selection process at each node’s split point, thereby augmenting the diversity and generalizability of the ensemble.

Neuro-symbolic artificial intelligence represents an avant-garde domain within the purview of artificial intelligence research, amalgamating the merits of conventional rule-based AI methodologies with the cutting-edge techniques of deep learning. Compared with deep learning models, symbolic models offer several advantages, including the need for very few input samples, effective generalization to new problems, and conceptually straightforward internal functions. While deep learning has garnered substantial acclaim for its prowess in extracting intricate features from data, particularly in domains like object detection and natural language processing, symbolic artificial intelligence distinguishes itself by its aptitude in codifying human-like reasoning processes. The overarching objective is to harness the capabilities of deep learning to extract features from data, which are then manipulated through symbolic methodologies, thereby capitalizing on the strengths of both realms.

In the present investigation, we synergistically integrated the application of CNN with RF, with Figure 3 delineating the training regimen. The data were initially ingested and refined; subsequently, they were partitioned into feature sets and target values and normalized employing the MinMaxScaler. A CNN architecture was delineated, comprising three convolutional layers and two fully connected layers, aptly designed for processing data with an inherent spatial structure. The convolutional layers served to distill features, which were subsequently mapped to the ultimate output via the fully connected layers. The input was convolved by the convolutional layers and then passed through the ReLU activation functions, flattened, and finally processed by the fully connected layers to generate the output. The model was subjected to a training regimen of 50 epochs, utilizing the mean squared error (MSE) loss function, with the Adam optimizer employed to assess the model, thereby computing pertinent evaluation metrics. The output emanating from the CNN was employed as feature inputs for an RF regression model, and an instance of an RF regressor was instantiated and trained with the training data. Within the scope of this paper, cross-validation was performed, finding that the number of feature vectors contemplated at each split was 17. The minimum number of samples at each internal node was established at 3, a precautionary measure to avert overfitting that may arise from an insufficiency of samples. The RF ensemble comprised 81 trees, with the understanding that an increment in the number of trees generally bolsters the model’s performance, albeit at the expense of heightened computational expenditure. Subsequent regression analysis was executed utilizing the RF regressor to accomplish the prediction and computation of a spectrum of evaluation metrics.

3. Results

3.1. Tensile Strength Test Results

The correlation among the process parameters and the resultant tensile strength is systematically tabulated in

Table 3. Tensile strength of SLM-formed 316L stainless steel.

NO.	Laser Power (W)	Scanning Speed (mm·s−1)	Hatch Spacing (mm)	Layer Thickness (μm)	Tensile Strength (MPa)
1	100	600	0.1	30	554.37
2	100	600	0.12	30	504.35
3	100	600	0.14	30	400.17
4	100	800	0.1	30	465.99
5	100	800	0.12	30	348.15
6	100	800	0.14	30	324.94
7	100	1000	0.1	30	333.54
8	100	1000	0.12	30	297.16
9	100	1000	0.14	30	242.88
10	200	600	0.1	30	627.15
11	200	600	0.12	30	632.50
12	200	600	0.14	30	615.40
13	200	800	0.1	30	617.42
14	200	800	0.12	30	618.89
15	200	800	0.14	30	608.66
16	200	1000	0.1	30	613.13
17	200	1000	0.12	30	598.25
18	200	1000	0.14	30	594.60
19	300	600	0.1	30	638.61
20	300	600	0.12	30	627.25
21	300	600	0.14	30	611.53
22	300	800	0.1	30	645.95
23	300	800	0.12	30	637.69
24	300	800	0.14	30	621.94
25	300	1000	0.1	30	654.02
26	300	1000	0.12	30	639.01
27	300	1000	0.14	30	628.03
28	100	600	0.1	30	434.82
29	100	600	0.12	30	368.51
30	100	600	0.14	30	285.16
31	100	800	0.1	30	320.43
32	100	800	0.12	30	221.24
33	100	800	0.14	30	196.41
34	100	1000	0.1	30	219.06
35	100	1000	0.12	30	172.51
36	100	1000	0.14	30	115.51
37	200	600	0.1	30	638.02
38	200	600	0.12	30	626.37
39	200	600	0.14	30	616.37
40	200	800	0.1	30	618.74
41	200	800	0.12	30	632.28
42	200	800	0.14	30	625.94

. It can be observed that, under a constant powder layer thickness, laser power exerts the most significant influence on the tensile strength of 316L stainless steel, and in conjunction with scanning speed and scanning spacing, jointly determines the tensile strength. When the laser power is too low, the scanning speed is too high, or the scanning spacing is too large, the energy input from the laser to the powder becomes insufficient, resulting in poor tensile strength.

To further expand the scope of prediction, relative density and Vickers hardness were incorporated into the input conditions as additional material properties, serving as a comparison with predictions based solely on process parameters. This integration enables a closer correlation between material properties and the predictive results of tensile strength. Figure 4 shows the curves of relative density, Vickers hardness, and tensile strength of the specimens. Overall, tensile strength is positively correlated with both relative density and Vickers hardness: the higher the relative density and hardness, the higher the tensile strength. This relationship, however, is not absolute. When two specimens have similar relative densities and Vickers hardness values, the one with the slightly lower figures may still exhibit higher tensile strength. This is because the factors governing relative density and Vickers hardness are complex, encompassing porosity, cracks, powder fusion quality, and other microstructural features.

Figure 5 shows the micro-morphology of pores in the specimens, illustrating that process parameters exert a decisive influence on pore formation and, consequently, on relative density. When the laser power is 100 W, the input energy is insufficient, resulting in a low melt-pool temperature and poor fluidity, wettability, and spreading capability. Consequently, numerous irregularly shaped process pores remain unfilled, severely reducing the relative density and leading to inferior mechanical properties. At laser powers of 200 W or 300 W, the increased energy input melts the metal powder more effectively. The improved wettability and fluidity of the molten metal enhance liquid-phase diffusion, markedly decreasing porosity. Furthermore, molten metal from the subsequent layer can infiltrate pores in the preceding layer, further diminishing solidification cracks and increasing relative density; thus, the specimens generally exhibit superior mechanical performance. Additionally, when laser power is low, increasing the input energy by reducing scan speed, hatch spacing, or layer thickness can also enhance relative density.

3.2. Tensile Strength Prediction Results

This study adopts a two-stage CNN–RF regression framework. First, the 6-dimensional input features (four process parameters and two auxiliary material properties) are normalized using Min–Max scaling and arranged into a tensor of shape (N, 1, F, 1). A lightweight CNN consisting of three convolutional layers is then constructed: the convolutional kernel sizes are 1 × 1, 3 × 1, and 5 × 1, the channel numbers are 1 → 4 → 32 → 16, the stride is 1, and padding = 1; each layer is followed by a ReLU activation. The flattened convolutional output produces a 560-dimensional vector, which is mapped by two fully connected layers to a 1-dimensional tensile strength prediction (fc1: 560 → 1) and a 16-dimensional deep feature vector (fc2: 560 → 16). In the first stage, the mean squared error between the output of fc1 and the measured tensile strength is used as the loss function. The CNN is trained with the Adam optimizer (learning rate 0.01), batch size 6, for 40 epochs, updating all CNN parameters through supervised learning to obtain a converged process–property feature extractor. In the second stage, the CNN weights are frozen, and only the 16-dimensional features obtained from forward propagation of the training samples are used as embedding representations, which are input to a random forest regressor for training. The main hyperparameters of RF are set as follows: number of trees n_estimators = 200, maximum depth max_depth = 15, maximum features max_features = “sqrt”, minimum samples for split min_samples_split = 4, minimum samples per leaf min_samples_leaf = 2, random_state = 42. During inference, new samples are first processed by the trained CNN to compute 16-dimensional embeddings, which are then fed to the RF to produce the final tensile strength prediction, enabling robust modeling of process–property relationships under small-sample conditions.

In the rigorous assessment of the model’s predictive efficacy, a triumvirate of evaluation metrics has been meticulously selected: mean squared error (MSE), mean absolute error (MAE), and R-squared (R²). The mean squared error (MSE) quantifies the mean of the squared discrepancies between the predicted and actual values, providing a measure of the prediction error’s magnitude. A diminutive MSE value is indicative of a reduced prediction error, thereby signifying a superior predictive performance of the model. The MAE serves as a metric that encapsulates the mean of the absolute differences between the predicted and actual values. This metric offers a direct reflection of the average prediction error’s magnitude. Consequently, a lower MAE value is correlated with a heightened level of prediction accuracy. Lastly, the coefficient of determination R² is employed to measure the proportion of the variance in the dependent variable that is predictable from the independent variables. R² provides an insight into the goodness of fit of the model, with values closer to 1 indicating a more precise fit to the data. MSE, MAE, and R² are calculated using Formulas (1)–(3):

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

(1)

$$\mathrm{MAE}={\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{X}}_{\mathrm{i}}-{\mathrm{Y}}_{\mathrm{i}}\right|}{\mathrm{n}}}$$

(2)

$${\mathrm{R}}^2=1-{\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{X}}_{\mathrm{i}}-{\mathrm{Y}}_{\mathrm{i}}\right)}^2}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{X}}_{\mathrm{i}}-\overline{{\mathrm{Y}}_{\mathrm{i}}}\right)}^2}}$$

(3)

In these formulas, $\mathrm{n}$ represents the total number of data points, ${\mathrm{X}}_{\mathrm{i}}$ represents the actual values, ${\mathrm{Y}}_{\mathrm{i}}$ represents the predicted values, and $\overline{{\mathrm{Y}}_{\mathrm{i}}}$ represents the mean of the predicted values.

The veracity of the model’s predictive accuracy was empirically substantiated through a series of 12 experimental datasets. As depicted in Figure 6, the red and black data points symbolize the congruence between the predicted and experimental values when employing a CNN in isolation and in conjunction with an RF, respectively. Notably, the CNN + RF data points exhibit a closer alignment to the graph’s diagonal, signifying a heightened proximity of predicted values to their experimental counterparts. This observation underscores a marked enhancement in the precision of the model’s predictive capabilities. Figure 7 presents a comparative analysis of the predictive evaluation metrics for both the CNN and the CNN + RF models. It is discernible that the MSE and MAE for the CNN + RF model significantly reduced from 0.00305 and 0.0505 to 0.00295 and 0.0344, respectively. These reductions correspond to a decrement of 3.28% and 31.88%, respectively. Concurrently, the R² witnessed a substantial increment from 0.2473 to 0.9576, which translates to an enhancement of 74.18%. This significant augmentation in the R-squared value is indicative of a substantial improvement in the reliability of the predicted values.

Figure 8 and Figure 9 show the comparison of predicted and experimental values and the comparison of evaluation metrics, respectively, after incorporating relative density and Vickers hardness as additional input conditions. For the CNN model, the MSE, MAE, and R² were 0.00246, 0.0427, and 0.515, respectively, while for the CNN + RF model, they were 0.000677, 0.0231, and 0.708. These results exhibit a consistent trend with the predictions based solely on SLM process parameters; however, a slight decrease in predictive reliability can be observed, as indicated by the reduction in R². This phenomenon is not uncommon, and its underlying reasons can be interpreted from two aspects. On the one hand, the newly added physical quantities may exhibit strong collinearity with existing input variables; for example, relative density is highly correlated with certain processing parameters (such as laser power and scanning speed). When the independent variables are highly correlated, regression or fitting models find it difficult to distinguish the weights of the true signal versus noise, leading to unstable parameter estimates and increased prediction variance, which reduces R². On the other hand, for small-sample datasets, adding feature dimensions can trigger the adverse effects of the curse of dimensionality. That is, with the number of samples unchanged, the functional complexity that the model needs to estimate or learn increases. If the new variables carry limited information or contain measurement noise, the model may fit noise as if it were signal, ultimately resulting in decreased generalization performance and a reduction in R².

The prediction errors of the CNN + RF hybrid model in estimating the tensile strength of SLM-produced 316L stainless steel can be primarily attributed to the following two aspects: Firstly, there are limitations at the data level. Experimental measurement errors and recording deviations in process parameters introduce data noise, while the limited small datasets may inadequately represent the complete distribution of material characteristics, resulting in insufficient model learning. Secondly, the model architecture has inherent constraints. The convolutional kernels of CNN may not fully capture multi-scale metallurgical features, and RF’s weight allocation for CNN-extracted features during ensemble decision-making may not be optimal, particularly when the sample distribution is uneven. Collectively, these findings demonstrate that the CNN + RF model is more adept at accommodating complex, nonlinear relationships and achieving heightened precision in predictions, particularly when operating with modest datasets.

4. Discussion

The presented model boasts a distinct advantage in its capacity to navigate the intricate interplay between six independent parameters and a single dependent predictive value. Traditional regression models often fall short in discerning the underlying logic inherent in such complex systems, while deep learning models, despite their prowess, frequently encounter challenges in rendering precise predictions when confronted with limited datasets. However, the CNN + RF methodology circumvents these limitations by harnessing the CNN’s prowess in capturing and synthesizing multidimensional features from the training data, thereby exemplifying the superior feature extraction capabilities of neural network architectures. Subsequently, the features extracted are fed into the RF regressor, which capitalizes on relatively simplistic internal regression algorithms when juxtaposed with the sophisticated algorithms employed in deep learning models for regression to augment the model’s predictive performance. This method combines the complementary advantages of CNN + RF feature extraction and classification capabilities.

In addition, on small datasets, RF can effectively use limited samples for training through Bootstrap Sampling and random feature selection, thereby improving classification accuracy [31,32]. This method can alleviate the overfitting problem caused by small datasets to some extent. Although CNN has a high demand for data volume, it can improve the generalization ability of the model on small datasets through data enhancement and other technologies, which has also been mentioned in previous studies [33,34]. The combination of CNN + RF can adjust the structure of CNN and RF parameters according to specific tasks, such as adjusting the number of convolutional layers of CNN, the number of decision trees of RF, etc., to adapt to different small datasets, which reflects the flexibility and scalability of the model. This is an important reason why this study can use 42 sets of data for prediction.

It should be noted that the proposed CNN + RF model still has several limitations. First, both the training and validation data originate from a single SLM machine and the same batch of 316L powder, and the sample size is relatively limited due to the cost of fabrication and mechanical testing. Therefore, the current results are better understood as a methodological validation within a specific equipment and material system, rather than a general conclusion applicable to all process conditions. Second, the model does not explicitly account for process noise or measurement uncertainties, and it has not yet been evaluated for transferability across batches, machines, or different material systems. Performance may degrade if there are significant changes in machine conditions, powder batches, or component geometry. Future work will combine more experimental data and multi-source simulation data to systematically investigate the model’s generalization ability and robustness, and explore integration with uncertainty quantification methods.

In the future, the CNN + RF model is expected to have a wider range of prediction applications in the engineering field, such as corrosion resistance prediction, fatigue performance prediction, etc. CNN can automatically extract complex features of materials, such as microstructure, chemical composition distribution, material microstructure, and defect characteristics, while RF can effectively classify and perform regression on these features to improve the accuracy of corrosion rate prediction, or model the relationship between complex features and fatigue life. Moreover, the prediction of the model may encounter the additive manufacturing technology with multiple materials and more complex process parameters, and face the high material cost, the smaller dataset caused by the high processing cost, and the training data are difficult to cover all conditions due to the dynamic change of material properties with the printing process. To this end, future improvements could be achieved through (1) introducing physics-constrained loss functions; (2) optimizing feature weights using attention mechanisms; and (3) incorporating cross-scale modeling approaches, such as phase-field simulation data, to further enhance prediction accuracy.

5. Conclusions

In the present investigation, a holistic predictive model was meticulously engineered, integrating CNN and RF algorithms, to elucidate the pivotal process parameters influencing the mechanical properties of 316L stainless steel fabricated via SLM. The model was designed to ingest laser power, scanning velocity, hatch spacing, and layer thickness as independent variables, with tensile strength serving as the dependent output variable. The ensuing conclusions are delineated as follows:

(1)

The synergistic integration of CNN and RF methodologies was demonstrated to be efficacious in prognostically estimating the tensile strength of SLM-formed 316L stainless steel. This amalgamation offers a robust and sophisticated modeling paradigm for this intricate endeavor.

(2)

In juxtaposition to the utilization of the CNN algorithm in isolation, the predictive outputs of the CNN + RF model exhibit a notable reduction in variance. Concurrently, the correlation coefficient was observed to escalate substantially, which is indicative of a marked enhancement in the precision of the model’s predictive capabilities.

(3)

The CNN + RF model leverages the complementary strengths of feature extraction inherent to CNN and the relatively straightforward internal regression mechanisms of RF, thereby effectively facilitating high-fidelity predictions for datasets of modest size.

(4)

When the number of samples is fixed, incorporating more additive manufacturing-related parameters into the prediction may lead to a decline in accuracy. Therefore, further optimization of the predictive model is required to better accommodate small datasets and multi-parameter conditions.