Machine Learning in predicting the properties of Ti-6Al-4V samples_preprint

Machine Learning application in predicting the properties of Ti-6Al-4V samples produced with Power Bed Fusion technology Quoc-Phu Ma1, Hoang-Sy Nguyen2*, Duy-Quy Vo3, Jiri Hajnys1, Jakub Mesicek1, Marek Pagac1, Jana Petru1 1Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, Vˇ SB-Technical University of Ostrava, Ostrava, Czech Republic. 2Becamex Business School, Eastern International University, Ho Chi Minh City, Vietnam. 3Department of Computer Science, Faculty of Electrical Engineering and Computer Science, Vˇ SB-Technical University of Ostrava, Ostrava, Czech Republic. *Corresponding author(s). E-mail(s): sy.nguy[email protected]; Abstract In the context of Additive Manufacturing (AM) with high-cost materials such as Ti-6Al-4V (Ti64), minimizing physical experimentation through predictive models offers a strategic advantage in reducing lead time and manufacturing costs. In view of this, the present study attempts to build a systematic framework to establish such a predictive compacity. In particular, eight supervised Machine Learning (ML) models are compared based on their performance in predicting critical physical properties of AM components, i.e., 3D surface roughness, relative density, and hardness. The curated dataset comprises both traditional dimensional printing parameters and dimensionless parameters. Specifically, in addition to the conventional Volumetric Energy Density (VED) and four primary printing parameters (laser power, hatching distance, scanning speed, and layer height), the study discusses two dimensionless numbers Π1and Π2for property prediction. This work underscores the role of selecting predictors and models in advancing data-driven process optimization, offering a scalable approach for reducing experimental overhead in metal AM. 1 Keywords: Powder Bed Fusion, surface roughness, relative density, hardness, Machine learning, process-structure-property, Ti64 1 Introduction Recent years have witnessed the growth in applying Additive Manufacturing (AM) technology in producing hard-to-machine Ti-6Al-4V (Ti64) alloy [1,2]. It is an alloy valued in aerospace and defense for its high strength-to-weight ratio, corrosion resistance, and thermal stability [3,4]. Yet these properties also complicate traditional manufacturing methods [5,6], making advanced techniques like Powder Bed Fusion (PBF) an essential alternative for processing [7]. The technology works on powder as stock materials and employs a laser source that can fuse (sinter or melt) powder particles together to fabricate a 3D object, which can have highly complex geometry [8]. Beyond titanium, PBF is also applied for printing various metals [9,10], including stainless steel, maraging steel, aluminum, Inconel, etc. The technology allows for the fabrication of highly complex designs with density approaching those of casted components, making it a valuable tool in modern industries. In metal printing with PBF technology, adjusting the printing process parameters can govern multiple complex physical phenomena that occur due to the rapid powder - liquid - solid transitions [11,12]. This includes the absorption and reflection of the laser power, heat conduction, heat radiation, fluid flow, material emission, vaporization, and chemical reactions [13,14]. In the existing literature, process parameters can be classified into four categories being the machine setup, laser setup, scanning procedure, and material properties [14]. The improper choice of process parameters can lead to the problems of lack of fusion, keyhole formation, gas porosity, crack, delamination, balling, and significant residual stress [15,16]. Different parameters such as laser power, scanning speed, hatch distance, scanning strategy, layer height, part orientation are among the most commonly studied process parameters [17–19]. For instance, increasing the laser power enlarges the melt pool, promoting better bonding [20]. This, in turn, increases the relative density and reduces residual stress. In addition, a high scanning speed does not allow enough time to fully melt the stock material, resulting in poor bonding and decreased hardness [21]. Similarly, increasing the hatch distance reduces the fusion of nearby powder particles within a single layer, leading to incomplete melting and a lower density in the printed part [22]. Alongside scanning speed and hatch distance, increasing the layer height can accelerate the printing rate. However, thicker layers carry a higher risk of incomplete melting, which can lead to higher surface roughness [23]. Process parameters directly affect the melt pool size, material fusion, and microstructure, thereby influencing the properties of the printed materials [24,25]. To control the properties of printed metal in general or Ti64 specifically, instead of focusing on single process parameters, other quality metrics such as Energy Density (ED) for linear, area, or volume are derived [26]. These metrics are particularly useful because they correlate many process parameters that are crucial for PBF technology with the output, usually printed properties. For example, Volumetric Energy 2 Density (VED) accounts for the whole amount of energy input by the PBF system to the print and is calculated with four most impactful process parameters, that is, laser power, scanning speed, hatching distance, and layer height. As reported in [27], for Ti64 printing, the common ranges for laser power is (70 - 100) W, scanning speed is (70 - 1800) mm/s, hatching distance is (50 - 140) µm, and layer height is (20 - 50) µm. From the same paper, the typical ranges for printing Ti64 alloy of existing commercial and self-built machines is between 30 J/mm3and 210 J/mm3. The dual (α-β) phase of Ti64 is directly affected by the energy or heat input and the rapid heating-cooling cycles of the PBF process. This, in turn, vastly influences the mechanical properties of printed Ti64 and results in a finer microstructure compared to its casted counterpart [28]. A review of the existing literature in [27] reported that the optimal range for relative density is more than 60 J/mm3, surface roughness is (61 - 80) J/mm3, microhardness is (61 - 70) J/mm3, while tensile strength is more than 90 J/mm3. It is worth noting that VED may not capture all aspects of the printed properties. For instance, while the density of printed Ti64 products reported in [29] and [30] was similar (both are higher than 99.5%), the VED levels were significantly different (150 J/mm3vs. 60 J/mm3). This discrepancy could be attributed to differences of either the density measuring method or the laser beam diameters. The latter results in variations in laser intensity and melt pool dimensions, which are not accounted for in the VED calculation. In addition, even when a number of samples are printed with the same VED, their final characteristics are influenced by individual parameters, as evidenced by different morphology, porosity, microstructure, and tensile strength of the Ti64 samples in [31–33]. In addition, other so-called dimensionless numbers can be investigated. Dimensional analysis is widely used in aerodynamics and heat transfer applications, but not as common in manufacturing, especially for PBF process. The formulation of dimensionless numbers helps provide a means for comparison across different PBF systems [34]. Accordingto [34], instead of having a formula that directly relate the input process parameters to the output properties, the formulation can be done with dimensional analysis. This reduces the number of process parameters needed for evaluation by combining groups of variables into a non-dimensional form that reflects specific physical phenomena [35]. This approach also highlights which subprocesses are important for further investigation. According to [36], there are four types of non-dimensional variables for PBF process that are the non-dimensional heat input, the Peclet number (Pe), the Marangoni number (Ma), and the Fourier number (Fo). However, over the years, numerous dimensionless numbers have been derived [34,37–40]. Most of the dimensionless numbers would require the information about the melt pool characteristics that are usually not available for users. For example, although both [35] and [39] derived their dimensionless numbers using the Buckingham Π theorem, the dimensionless numbers in [35] attempt to correlate material porosity solely with process parameters and material properties. In contrast, those in [39] focus on the fabrication of lattice structures, requiring more detailed information about the melt pool. It is worth noting that information about the melt pool can help incorporate important physical phenomena occurring during the PBF process, such as evaporation, 3 recoil pressure, buoyancy and capillary forces, Plateau-Rayleigh instability, Marangoni convection, and temperature-dependent material properties [41,42]. The variety of dimensionless numbers in the existing literature arises from different authors attempting to incorporate various process parameters relevant to control and predict specific output properties, in order to cope with the complex nature of the PBF process. From another perspective, Machine Learning (ML) has been extensively studied by researchers to advance AM in five key areas: Design for Additive Manufacturing (DfAM), material analytics, defect detection and monitoring, process modeling and control, and sustainability [43]. A bibliometric analysis of 10,054 articles published in 20 years up to 2020 across five major databases (ACM, IEEE Xplore, ScienceDirect, SpringerLink, and Scopus) reveals ML’s significant contributions to AM, particularly in detection, monitoring, prediction, and process optimization. The study in [43] highlights that quality-related topics dominate this research, with frequent references to keywords such as property, porosity, defect, and monitoring. In general, ML models learn patterns from established datasets to map inputs to outputs, enabling the generation of desired outputs based on new inputs provided by operators. This capability enables real-time decision-making. Moreover, ML models can be continually improved by updating them with new data from ongoing experiences or additional inputs [44]. Through Transfer Learning (TL), the learned knowledge can also be generalized and applied to similar tasks [45]. It is particularly advantageous for AM due to the high costs associated with acquiring data from printing and sample measurements. In recent years, ML has garnered significant attention in the research community as an efficient alternative for processing large AM datasets. Compared to computationally expensive multi-physics and multiscale simulations [46,47], ML offers more efficient processing and deeper insights into AM processes [48,49]. However, it should be noted that results from numerical simulations complemented with experiments [50] can serve as a valuable data source to guide ML models for better performance. Recent studies have applied statistical and ML methods to predict quality metrics in PBF AM. For example, Toprak [51] combined DoE, and ML to predict hardness of AlSi10Mg using 27 samples, where Support Vector Machine (SVM) achieved the highest accuracy (R2= 0.73). Gor et al. [52] compared Neural Network (NN), Knearest Neighbor (KNN), SVM, and Linear Regression (LR) as a baseline for SS316L density prediction using multi-source data, with Feed Forward NN (FFNN) reaching R2= 0.95 but high error, while SVM offered a better balance result of R2= 0.923. From another perspective, Zhu et al. [53] employed conditional generative adversarial network (GAN) for data augmentation to enhance Vickers hardness prediction of high-entropy alloys, improving DNN performance from R2= 0.71 to 0.84. In addition, Maitra and Shi [54] predicted 2D surface roughness (Ra) of Ti-6Al-4V using 1211 data points and additional power morphology (Average Particle Size (APS) and Variability in Particle Size (VAR)) parameters, where Gaussian Process Regression (GPR) and NN performed best (Root Mean Square Error (RMSE) of 0.51 µm and 0.58 µm). La F´e-Perdomo et al. [55] applied Box-Behnken design to establish a dataset for SS316L property prediction with ML models, with Gaussian Process Regression (GPR) best for surface roughness, ensemble model for relative density, and NN for tensile strengths and hardness (all are with accuracy higher than 90%). Later, group of the 4 same author [56] optimized NN and Adaptive Network-based Fuzzy Inference System (ANFIS) using Non-dominated Sorting Genetic Algorithm (NSGA-II) for SS316L surface roughness prediction, achieving R2= 0.984 and 0.939, respectively. Benchmarked from AlSi10Mg properties (relative density, surface roughness, and hardness) based on 390 data points, Alamri et al. [57] proved that NN consistently outperformed Support Vector Regrssion (SVR), Kernel Ridge regression (KRR), Random Forest (RF), and Lasso regression with R2up to 0.772. On a wider scope, Akbari et al. [58] compiled a large dataset (1600 points) across AM metals with various information about the materials and machines to predict the printed properties (strengths, surface roughness, hardness), and demonstrated relatively high accuracy of R2minimum 0.85 with RF, Gradient Boosting (GB), and NN. Interestingly, Muhammad et al. [59] used Deep Learning (DL) to predict AlSi10Mg average 3D surface roughness (Sa) from 3D profilometry data measured on 40 round bar specimens, taking into account the location of the samples on the baseplate and measuring locations, with prediction within 5% experimental error. Finally, Toorandaz et al. [60] introduced in-situ Saprediction using melt pool data obtained from photodiode sensor, where RF and Extreme Gradient Boosting (XGB) outperformed other models in comparison in terms of F1-score. Inspired by existing literature, this study employs ML to predict the properties of Ti64 components produced using PBF technology. The measured properties include 3D surface roughness, relative density, and macrohardness. Four quality metrics are utilized for the ML studies: the four printing parameters (laser power, scanning speed, hatching distance, and layer height), the VED and two dimensionless numbers. These metrics, along with the measured properties of the components, are used to train ML models and to make predictions. There are two statistical regression models LR, and Ridge Regression (Ridge) employed together with six ML models, that is, SVR, Decision Tree (DT), RF, GB, XGB, and Adaboost (AB), for a better view to the prediction performance. The study aims to evaluate the performance of various ML models in predicting the specified properties. Ultimately, by leveraging the advantages of ML models, this approach seeks to significantly reduce the costs associated with physical testing and computational time. The paper is organized as follows. Section 1provides the necessary background to understand the research topic. Section 2details the materials and methods used in this study, including the process parameters, quality metrics, sample fabrication, property measurements, and the ML models that are employed. Section 3presents the results of the property evaluation and compares the performance of various ML models in predicting the properties based on the provided data. Finally, Section 4concludes the paper with an outlook on potential future research directions. 2 Materials and Methods 2.1 Volumetric Energy Density and dimensionless number The quality of a product from PBF system depends on several process parameters and their interactions. Thus, it is inadequate to consider each parameter separately while setting up the printing parameters. Rather, it is suggested in the existing literature 5 to look at the parameters as a whole using a measure such as the VED, which is formulated as follows E=P vht,(1) where there are the VED E(J/mm3), the laser power P(W), the scanning speed v (mm/s), the hatching distance h(mm), and the layer height t(mm). It should be remarked that E, which is later interchangeably noted as VED, is a product of four key process parameters in PBF. Given this, two completely different sets of printing parameters can have the same Evalue as a product. For example, even if both P and vincrease twofold, Ewill remain the same. In general, a higher Einput deepens and widens the size of the melt pool, which can result in different microstructure and melt pool [61]. Nevertheless, Ehas become the most popular metric for evaluating the effect of printing parameters on the properties of PBF-printed products [27]. In addition to the four basic parameters used in Equation (1), more parameters can be taken into account considering the dynamic of the energy distribution within the molten pool. The measure is called a dimensionless number, a scalar used in fluid mechanics and heat transfer studies to describe the thermo-dynamical behaviors of a system [62]. A dimensionless number is presented in [35] as Π1=CpP kv2h,(2) where the thermal properties of the material are additionally considered, that is, the specific heat Cp(J/kg ·K), and the thermal conductivity k(W/mm ·K). To better understand the physical meaning of Π1, we can consider an additional concept of dwell time τ=d v,(3) where the dwell time τ(s) is defined as the time the laser beam travels a distance equal to its diameter d(mm). Combining Equation (1), Equation (2) and Equation (3), it is possible to rewrite the dimensionless number Π1as Π2=Cp kEτ. (4) From Equation (4), we can observe that the dimensionless number is a function of the material’s thermal properties, V ED, and the dwell time. The dimensionless number Π2is more versatile than Π1because it also considers the diameter of the laser beam and the layer height [35]. It should be noted that, as opposed to VED, the dimensionless numbers are unitless. In this study, we utilize these three quality metrics to evaluate the properties of the final product. 2.2 Design of Experiment and sample fabrication The machine that is used for printing is Renishaw AM400 with the build volume of 250 ×250 ×300 mm3and the Ti64 powder supply from the same company [63]. 6 Fig. 1: SEM/BSE image of the Ti64 powder in used. The shape and size of the powder can be observed in Scanning Electron Microscopy (SEM)/Backscattered Electron (BSE) image in Figure 1. As can be observed from Figure 1, the Ti64 powder is characterized by spherical particles that is suitable for spreading on the baseplate. From the manufacturer, the composition of the material (% w/w) is Ti (80 - 90)%, Al (6 - 6.5)%, and V (3.8 - 4.5)%. The printing is done within the inert atmosphere of argon. The printing parameters are listed in Table 1. Table 1: Printing parameters. Power - P(W) 200; 250; 300 Hatching distance - h(µm) 75; 100; 125 Scanning speed - v(mm/s) 600; 700; 800 Layer height - t(µm) 10; 30; 60 Strategy Meander As can be seen in Table 1, each key parameter for calculation of V ED in Equation (1) has three values to vary for the calculation of the quality metrics. By combining the parameters, we have printed in total 81 samples for the study. However, for samples with 10 µm layer height, they inherit cracks due to the excessive thermal stress. It should be noted that, in this study, we aim to develop printing parameters as well for practical use. Samples with cracks, thus, are not considered to be successful print. Besides, this hinders the proper measurement of relative density and surface roughness. While the microhardness of the bottom surface can be measured, in order to ensure the uniformity of the study, samples printed in the 10 µm batch are omitted, leaving 54 samples for the study. Their parameters and according quality metrics are listed in Table 2. 7 Table 2: Configurations of printed parameters and corresponding E, Π1, and Π2for samples with layer height of 30 µm and 60 µm. P(W)h(µm)v(mm/s)t(µm)E(J/mm3) Π1(−) Π2(−) 200 0.075 600 30 148 598 1096 200 0.075 700 30 127 439 805 200 0.075 800 30 111 336 617 200 0.1 600 30 111 448 822 200 0.1 700 30 95 329 604 200 0.1 800 30 83 252 462 200 0.125 600 30 89 359 658 200 0.125 700 30 76 264 483 200 0.125 800 30 67 202 370 250 0.075 600 30 185 747 1370 250 0.075 700 30 159 549 1007 250 0.075 800 30 139 420 771 250 0.1 600 30 139 561 1028 250 0.1 700 30 119 412 755 250 0.1 800 30 104 315 578 250 0.125 600 30 111 448 822 250 0.125 700 30 95 329 604 250 0.125 800 30 83 252 462 300 0.075 600 30 222 897 1644 300 0.075 700 30 190 659 1208 300 0.075 800 30 167 504 925 300 0.1 600 30 167 673 1233 300 0.1 700 30 143 494 906 300 0.1 800 30 125 378 694 300 0.125 600 30 133 538 987 300 0.125 700 30 114 395 725 300 0.125 800 30 100 303 555 200 0.075 600 60 74 598 548 200 0.075 700 60 63 439 403 200 0.075 800 60 56 336 308 200 0.1 600 60 56 448 411 200 0.1 700 60 48 329 302 200 0.1 800 60 42 252 231 200 0.125 600 60 44 359 329 200 0.125 700 60 38 264 242 200 0.125 800 60 33 202 185 250 0.075 600 60 93 747 685 250 0.075 700 60 79 549 503 250 0.075 800 60 69 420 385 250 0.1 600 60 69 561 514 250 0.1 700 60 60 412 377 250 0.1 800 60 52 315 289 250 0.125 600 60 56 448 411 250 0.125 700 60 48 329 302 250 0.125 800 60 42 252 231 300 0.075 600 60 111 897 822 300 0.075 700 60 95 659 604 300 0.075 800 60 83 504 462 300 0.1 600 60 83 673 617 300 0.1 700 60 71 494 453 300 0.1 800 60 63 378 347 300 0.125 600 60 67 538 493 300 0.125 700 60 57 395 362 300 0.125 800 60 50 303 277 8 The properties of the printed samples in terms of surface roughness, relative density, and hardness are measured and later subjected to the DoE and ML study. The sample is a prism with 1-mm rounded edges sizing of 10 x 10 x 20 mm3. Their positions on the baseplate are shown in Figure 2. Fig. 2: Distribution of the printed samples on the baseplate. As shown in Figure 2, we print a total of three builds, each containing 27 samples, making up the 81 samples as planned. Each of the samples is marked with a number for later handling purposes. The separation into three builds is necessary due to the printer’s constraint of having only one layer height in one build. Each sample is marked with a number for easier classification. The samples are printed directly on the baseplate and are removed after printing with Wire Electrical Discharge Machining (WEDM) cutting. WEDM leaves the bottom surface sufficient roughness for subsequent hardness test. 2.3 Machine Learning model In this study, a total of eight models are employed. Two statistical models are LR and Ridge (statistical). Six ML models are SVR, DT, RF, GB, XGB, AB. It should be noted that LR and Ridge assume the linear relationship between the inputs and outputs, which serve as the baseline for performance comparison with other ML models. The ML models are chosen with the consideration that they can handle non-linear and small-sized datasets. Table 3outlines the ML algorithms that are employed in this study with their corresponding hyperparameters that are tuned for optimal prediction in this study. Out of the selected models, LR is the simplest regression method. It assumes a linear relationship between independent and dependent variables attempts to fit a straight line to the dataset while minimizing the sum of squared errors. Thus, it cannot capture non-linearity. Ridge extends LR by adding an L2 regularization term to reduce variance and overfitting, making it effective for multi-collinear or high-dimensional datasets, though it still assumes linearity. From another perspectives, SVR applies SVM principles to regression, fitting data within an epsilon margin and can hand both linear and non-linear relationships via kernels such as linear, polynomial, and Radial 9 Table 5: The optimal ML model for predicting the roughness Sawith their corresponding metrics. V ED Π1Π24pars AB (80-20) XGB (80-20) RF (80-20) SVR (80-20) R20.13 0.47 0.47 0.02 MAPE (%) 25.16 21.87 18.67 27.38 MAE 3.76 3.09 3.2 3.79 Table 6: The optimal ML model for predicting the relative density with their corresponding metrics. V ED Π1Π24pars AB (80-20) XGB (80-20) GB (50-50) RF (70-30) R20.55 0.21 0.14 0.56 MAPE (%) 0.12 0.22 0.25 0.2 MAE (0) (0) (0) (0) Table 7: The optimal ML model for predicting the hardness with their corresponding metrics. V ED Π1Π24pars SVR (60-40) SVR (60-40) SVR (60-40) XGB (80-20) R20.01 (0) 0.01 0.41 MAPE (%) 2.67 2.66 2.66 1.79 MAE 13.65 13.59 13.61 9.11 that even though R2is selected as primary indicator for the model performance, it is not necessary that the performance of the model with highest R2is the best. For example, when predicting Sawith Π1, GB (90-10) results in a very high R2of 0.53. However, its performance is much worse when the training ratio is 10% less. Indeed, GB (80-20) only exhibits R2of -0.25, indicating that the model predicts worse than the mean of the target output. This may be dedicated to the underfitting problems. In this manner, XGB is chosen because of its consistent positive R2values, that is, (90-10) of 0.52, (80-20) of 0.47, and (70-30) of 0.23. From Table 5, it can be drawn that for predicting the Savalues, the most effective models are XGB (80-20) with Π1, and RF (80-20) with Π2. Similarly, for predicting the relative density, see Table 6, the best models are AB (80-20) with V ED, and RF (70-30) with 4 pars. It should be noted that the MAPE and MAE results are remarkably low. To understand this, it is noteworth to emphasize that the relative density input into ML models for training purposes are smaller than 16 1. The target variable (relative density) varies within a very narrow range of (0.979 - 0.996), except for an outlier at 0.944 (see distribution in Figure 4, where the values are multipled with 100 and assigned % for better presentation). For such a scenario with low variance, even a prediction that is slightly off the true values can result in considerably low MAPE and MAE, since the magnitude of the absolute errors are small. MAPE and MAE could not fully reflect the model performance for this scenario. Therefore, they have to be accompanied by the R2metric that better reflects the true data patterns. Finally, for hardness prediction, XGB (80-20) performs the best for 4 pars. The results of this study are in agreement with [65] that only nonlinear ML models, i.e., XGB, RF, AB and SVR can perform well with such a highly nonlinear dataset as depicted in Figure 4. Regarding the prediction accuracy, for each predicted property, there is at least one ML model that can yield the R2value of more than 0.4, which is as well the baseline for prediction in paper [65]. The parity plots that show performance of the ML models are presented in more details in Figure 6. They correspond to the best models summarized in Table 8, Table 9, and Table 10. In general, it can be observed that all of the selected models achieve satisfactory performance, with minimal observed error. Parity plots of the relative density prediction inherit more tightly clustered data points, which is in agreement with the low variance shown by the low MAPE and MAE measures. On the other hand, parity plots of roughness Saand hardness prediction show more balanced and scattered datapoints to the two sides of the reference line, which is reflected already in the higher measures of MAPE and MAE. In addition, for prediction of relative density and hardness with 4 pars models, it is possible to evaluate the feature importance as there are multiple input process parameters. This analysis shows how significant these process parameters in predicting the desired output, which can be seen in Figure 7. It can be drawn that for the RF model, scan speed plays the most significant role in predicting the relative density, followed by layer height. Meanwhile, power and hatch distance have similar and the least importance. On the other hand, for prediction of the hardness with XGB, power has the highest influence, followed by layer height, hatch distance, and scan speed. However, it should be noted that these feature importance may not reflect the underneath physical dependency between process parameters and the measured quality [66]. Rather, they show the statistical influence of features on the model’s internal decision-making process. This, indeed, can be biased depending on the distribution of the input data distribution, and setting of the hyperparameters of the models. It can be drawn from the above results that, despite using the same set of hyperparameters for tuning, the ML models exhibit different performance in predicting different printed properties. This observation is consistent with the “no-free lunch” theorem [49] of ML deployments since no single ML model can be universally optimal for all types of problems. This is because the input data distributions of the three properties under evaluation are different due to their nature (see Figure 4), leading to different pattern extraction for each property. In addition, only non-linear ML models can effectively capture the pattern of the input data, which aligns well with the findings in previous studies by Toprak [51] and Gor et al. [52]. 17 Fig. 6: Model performance in terms of predicted values versus the true. From top to bottom: roughness Sa, relative density, and hardness. The discontinuous red line is the reference line where predicted values are equal to true values. 18 Fig. 7: Feature importance of the process parameters. From top to bottom: RF (7030) for prediction of relative density, and XGB (80-20) for prediction of hardness. Due to the limited input data, bootstrapping is conducted to examine how the ML models employed to assess the reliability and generality of the findings, as can be seen in Figure 11. The plots are characterized by the actual value from the experiments (purple line), the mean value of the predictions (discontinuous red line), the 95% confidence interval (green zone), and the density curve which is the smoothed version of the histogram to show the overall shape of the distribution. In the roughness prediction, the absolute error between the predicted mean of 17.181 µm and the actual value of 17.847 µm is 0.67 µm. In addition, the actual value is within the 95% confidence interval, which is a plus side. However, the confidence interval is almost 14 µm which is significantly high in comparison with the actual value of 17.847 µm. This can be interpreted that if the technical requirement for the surface of a component is 15 µm, then the prediction with 95% confidence will fall 19 between 10 µm and 24 µm. Even though this is statistically correct, the model is not sharp enough from the practical viewpoint. This partially reflects that the selected parameters are not be able to fully capture the complexity of the factors that affect the roughness. Additionally, other factors such as melt pool stability [54], and powder morphology [60] can be considered. On the other hand, for relative density prediction, the absolute error between the predicted mean and the actual value is nearly zero. The predicted mean also falls within a relatively narrow confidence interval, from 0.989 to 0.994, meaning that the predicted error is small. From the quality control perspective, this is acceptable because it can significantly reduce the need for physical measurements. It also indicates that the selected parameters play a significant role in determining the relative density and are well-suited this task. Last but not least, regarding hardness prediction, the predictions are highly consistent within a relatively narrow confidence interval between 502 HV 30 and 528 HV 30. However, the predictions collectively deviate from the actual value, which lies entirely outside the interval on the higher side. In other words, the model is overly confident in a result that is not correct. This suggests that the parameters used are not appropriate, or perhaps have little influence, on hardness, highlighting the need to explore alternative printing parameters that may be more relevant. Additional predictors could include melt pool radiation intensity data [67] or cooling rate [68], both of which directly affect microstructure formation in printed parts and subsequently the hardness level. Overall, even though the R2measures for the assessed ML models in this study are above 0.4 in comparison with the baseline value in [65], and the bootstrapped predictions show reasonable initial results, there remains a significant room for improvement after addressing the quantity and quality limitation of the input data. Specifically, the number of data points can be increased, or more complementary process parameters can be included to provide a more complete picture of the underlying physics, facilitating better prediction. Regarding quantity improvement, GAN can be employed for data augmentation to improve R2measure for Vickers hardness prediction as reported in [53]. This highlights the potential of using synthesis data to overcome data scarcity. Another approach is to increase the number of prints and physical measurements. Expanding the inhouse data ensures its uniformity owing to the controlled experimental background (known printing setup, material, machine, etc.). However, it is inherently costly. On the other hand, curating data from published literature following [57,58] is more timeand cost-effective. Nevertheless, the data is usually in inconsistent formats, with differences in experimental setups, and the possibility of missing critical input features. This requires careful data cleaning and feature selection. In addition, from the quality improvement perspective, to improve the prediction of surface roughness (both 2D and 3D), process-related features such as powder morphology (APS and VAR) [54], or melt pool data [60] could provide the ML models with more informative inputs. These parameters indeed influence the surface roughness and could therefore lead to more accurate predictions. Ultimately, the most effective approach is to combine both the quantity and quality improvement. 20 4 Conclusions and future works Inspired by the motivation to reduce the cost for AM, especially for expensive and hard-to-machine alloys such as Ti64, a dataset was established to predict the possible desired physical properties of the printed parts. Throughout the whole study, eight different ML models were compared and discussed. The physical properties of the printed parts that were examined are 3D surface roughness, relative density, and hardness. The below conclusions can be drawn: •For prediction of the 3D surface roughness, Π1and Π2can be used as the best predictors, with the XGB and RF models outperforming the rest. •For prediction of the relative density, traditional predictors, i.e., VED and the four printing parameters (P,h,v,t), yielded the best results, implying that these features are more suitable for this type of structured data. The best-performing models in this case are AB and RF. •For prediction of the hardness, only the four printing parameters proved to be effective predictors, with XGB showing the best performance among the tested models. •In agreement with conventional ML practices, the selected models demonstrate stable and reliable performance when the training-testing ratio is between 70-30 and 80-20. •Bootstrapping study reveals as well that the relative density can be the most reliably predicted with the current process parameters. As for the 3D surface roughness and the hardness, additional parameters of the melt pool and powder would be helpful for improving the prediction accuracy. From the obtained results, it can be concluded that the predictive success of ML models for different material properties is highly dependent on the distribution of each target dataset. This provide a foundation for applying ML techniques in the optimization of manufacturing parameters, with the potential to significantly reduce experimental costs and accelerate process development. 21 Acknowledgements. This article was funded by the European Union under the REFRESH – Research Excellence For REgion Sustainability and High-tech Industries project number CZ.10.03.01/00/22 003/0000048 via the Operational Programme Just Transition. It was also completed in connection with the project Innovative and additive technologies for sustainable energy industry”, registration no. 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Materials Design 113, 331–340 (2017) https://doi. org/10.1016/j.matdes.2016.10.037 25 Fig. 10: Model performance heatmap for hardness. 32 Fig. 11: Distribution of bootstrapped predictions. From top to bottom: for roughness, relative density, and hardness. 33