Machine Learning and Uncertainty Quantification for Predicting Weld Bead Geometry of AISI 304L in Micro-Size A-TIG Welding

Machine Learning and Uncertainty Quantification for Predicting Weld Bead Geometry of AISI 304L in Micro-Size A-TIG Welding | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Machine Learning and Uncertainty Quantification for Predicting Weld Bead Geometry of AISI 304L in Micro-Size A-TIG Welding Mahdi Mazloom Farsibaf, Seyed Moein Fareghi, Kiana Arteshyar, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9530256/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Machine learning (ML) modeling of Activated Tungsten Inert Gas (A-TIG) welding is challenged by the limited availability of experimental data. Within this research, uncertainty quantification of ML-based predictions of weld bead geometry (WBG) was investigated for AISI 304L stainless steel (SS304L) welded with six micro-sized activating fluxes (SiO₂, TiO₂, Al₂O₃, ZnO, CuO, CaCO₃). A design Matrix consisting of 45 runs was conducted, and depth of penetration (DOP), weld bead width (WBW), and the DOP-to-WBW (D/W) ratio were selected as evaluation parameters of WBG. Two predictive approaches were considered: Ridge regression as a linear baseline and Extreme Gradient Boosting (XGBoost) to capture nonlinear effects. Ridge regression provided moderate predictive performance, whereas XGBoost demonstrated superior accuracy with a determination coefficient (R 2 ) of 96%. Experimental results confirmed SiO₂ as the most effective flux, achieving a depth-to-width ratio (D/W) of approximately 0.794 at 160 A, consistent with the mechanism of flux-induced arc constriction and Marangoni reversal that enhances DOP. Uncertainty quantification (UQ) was performed using quantile regression. 90% prediction intervals (PIs) achieved empirical coverages between 56% and 78% across targets (worst for DOP). The correlation between interval width and prediction error indicated that the UQ framework provided informative, though under-confident, estimates of predictive reliability. These results establish a combined experimental–computational approach for uncertainty-aware modeling of A-TIG weld geometries, supporting more reliable process design and advancing the integration of ML in welding modeling. A-TIG welding Weld bead geometry Modelling Machine learning XGBoost and Ridge regression Uncertainty quantification Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 1- Introduction Tungsten Inert Gas (TIG) is widely used for high-quality, defect-sensitive joints because it produces a controllable, stable weld pool using a non-consumable tungsten electrode and an inert shielding gas [ 1 ]. The TIG welding process is widely used in industries such as aerospace, petrochemical, and medical equipment manufacturing due to its high precision and excellent surface quality [ 2 ]. It is also commonly applied for welding thin metals and special alloys like aluminum in the automotive and food industries [ 3 ]. However, conventional TIG has practical limitations for thicker sections: single-pass penetration is shallow (typically ≈ 2–3 mm), deposition rates are low, edge preparation requirements are strict, and travel speeds are relatively slow, limiting the degree of welding automation and making multi-pass welding necessary for many structural applications [ 4 ]. These constraints increase cycle time and cost when welding medium-to-thick components [ 5 ]. Several alternative and hybrid approaches have been introduced to address the inherent limitations of TIG welding. Techniques such as laser and electron-beam welding offer deep penetration at high travel speeds, while hybrid methods such as laser-arc and ultrasonic-assisted TIG merge energy sources or additional forces to enhance penetration, minimize the heat-affected zone (HAZ), and improve overall productivity. Such methods can address specific industrial needs but often require specialized equipment or present new process-control challenges that complicate adoption in standard shop floors. Activated TIG (A-TIG) offers a practical, low-cost route to deeper single-pass penetration by applying activating fluxes (e.g., TiO₂, SiO₂, Fe₂O₃) to the workpiece prior to welding [ 6 ]. These fluxes promote arc constriction, alter surface-tension gradients (reversing Marangoni flow), and increase current density at the arc root, collectively concentrating heat toward the joint center and producing deeper, narrower welds with reduced HAZ and distortion [ 7 ]. Several experimental and optimization studies have characterized A-TIG performance and flux effects. Singh and Khanna [ 7 ] reviewed process fundamentals and reported large penetration gains; Rana et al. [ 8 ] demonstrated significant penetration and mechanical-property improvements across different flux chemistries and TIG variants. These studies demonstrate that flux chemistry and process parameters significantly influence weld geometry. However, most previous research relies on traditional regression techniques (such as ANOVA), focusing primarily on nano-flux formulations or isolated parameter variations, rather than employing comprehensive, systematic predictive modeling that spans across both Flux composition and process parameters. In recent years, ML has increasingly been applied to welding research for predicting bead geometry, penetration depth, and mechanical properties. Common approaches include artificial neural networks (ANNs), support vector machines (SVM), and genetic algorithms (GA), which have demonstrated improved predictive accuracy over traditional regression methods [ 9 , 10 ]. However, these models are often treated as black boxes, limiting interpretability, and they rarely account for nonlinear parameter interactions in a systematic way. Furthermore, most ML applications in welding focus on macro-process optimization or defect detection, with relatively few studies targeting the D/W ratio that directly governs penetration efficiency [ 11 ]. At the same time, incorporating UQ into ML frameworks has become increasingly important for welding applications. Unlike conventional predictive models that yield only deterministic point estimates, UQ-enabled methods such as Monte Carlo simulation, Bayesian inference, and quantile regression provide probabilistic outputs with confidence intervals [ 12 ]. This additional layer of information is critical for handling the inherent variability of processes like A-TIG welding, where arc instabilities and thermofluidic fluctuations can significantly affect penetration behavior. Much of the recent literature has emphasized nano-sized fluxes because of their high surface area and reactivity; however, nano-fluxes can pose handling, dispersion, and scalability issues in practice, motivating investigation of micro-sized alternatives [ 13 ]. The present study addresses these gaps by experimentally evaluating six micro-structured activating fluxes (SiO₂, TiO₂, Al₂O₃, ZnO, CuO, CaCO₃) in A-TIG welding of SS304 L. A structured full-factorial design, augmented with additional tests for broader coverage, was employed for a total of 45 experimental runs to examine the effects of welding current and flux type. Additionally, data-driven predictive models for weld geometry, including DOP, WBW, and the D/W ratio, were developed. Ridge regression was utilized as an interpretable linear baseline, while XGBoost was applied to capture nonlinear interactions. To enhance decision-making, UQ through quantile regression was incorporated, providing probabilistic PIs for risk-aware choices. To our knowledge, this study is among the first to combine A-TIG experimentation with micro-sized fluxes, explicit machine learning-based prediction, and UQ, specifically focused on the practical D/W metric. 2- Materials and methods In this investigation, SS304L austenitic stainless steel was chosen as the base material due to its wide availability, corrosion resistance, weldability, and mechanical robustness. These characteristics, together with ready availability and ease of fabrication, make this alloy an appropriate base material for assessing the effects of activating fluxes on bead morphology and penetration [ 14 ]. The material’s chemical composition and mechanical properties are listed in Fig. 1. Test specimens (100 mm × 50 mm × 5 mm) were welded using a bead-on-plate method without filler material on a Gam Electric PSQ250 AC/DC welding machine, as depicted in Fig. 2. The torch travel speed was kept constant to investigate the effects of welding current and flux composition. A paste-like mixture was prepared using micro-sized flux powders (nominal 25–30 µm) and methanol at 0.2 g·mL⁻¹ and magnetically stirring the suspension at 600 rpm for 40 min at room temperature (≈ 25°C), followed by a 3-minute settling period. Representative powder samples were selected at random, and their particle-size distributions were confirmed by particle analysis, validating the nominal 25–30 µm range reported for the powders by the manufacturer. The flux paste was brushed onto a masked 100 × 10 mm area, which was defined using two strips of adhesive tape, and applied to a uniform thickness of 0.2 mm, measured with a filler gauge. The experimental input parameters are summarized in Table 1. Table 1 TIG input parameters Welding Parameters value Electrode Thoriated Tungsten 2.4 mm Gas Flow Rate 10 L.min − 1 (99.9% Argon) Torch Travel speed 145 mm/min Current 80,100,120,140,160 A Arc length 3 mm After completing the welding process, the specimens were sectioned transversely to prepare cross-sectional samples for metallographic examination. Cross-sectional Specimens were prepared according to ASTM E3. Cross-sectional images were captured with an OLYMPUS-530 optical microscope at 200× magnification, and DOP and WBW were measured using ImageJ. The welds were visually defect-free, consistent with ISO 17637 visual testing acceptance criteria. The screening test determined the highest and lowest effective currents that impact DOP and WBW in A-TIG welding, guiding subsequent detailed experiments. Experimental A-TIG studies report large sensitivity of penetration and bead shape to both Flux composition and process settings. Then, a structured experimental matrix was conducted to quantify how activating flux chemistry and welding current affect A-TIG weld geometry. The study began with a screening test: an initial full-factorial matrix (30 runs) was executed in JMP v18.0.1 to map main effects and two-way interactions between factors. To minimize systematic bias, the experimental runs were performed in a randomized order. The matrix was then augmented by 15 additional random runs (total n = 45) to enrich sampling near design boundaries, include intermediate current conditions and selected replicates, and provide greater data density for machine-learning training and UQ. The final full-factorial matrix (factors, levels, and measured responses: DOP, WBW, and D/W ratio) is summarized in Table 2. Table 2 Custom experimental design matrix and corresponding measured outputs Test number Current (I) Flux type DOP (mm) WBW (mm) D/W ratio 1 100 Sio2 2.558 4.316 0.592 2 100 Tio2 1.883 4.325 0.435 3 100 CaCo3 1.474 5.024 0.293 4 120 CaCo3 1.673 5.287 0.316 5 80 Al2O3 0.910 4.140 0.219 6 120 Tio2 2.110 4.948 0.426 7 120 Tio2 2.313 5.120 0.451 8 140 zno 1.779 6.743 0.263 9 100 zno 1.258 4.556 0.276 10 120 Al2O3 1.587 5.187 0.305 11 140 Al2O3 1.714 7.308 0.234 12 100 Cuo 1.736 4.354 0.398 13 140 CaCo3 1.895 6.574 0.288 14 100 Sio2 2.321 4.526 0.512 15 140 Tio2 3.003 6.105 0.491 16 140 Cuo 2.594 6.070 0.427 17 100 Al2O3 1.400 3.725 0.375 18 100 Cuo 1.787 4.259 0.419 19 120 zno 1.502 5.835 0.257 20 100 Tio2 1.574 4.302 0.365 21 140 Sio2 3.988 5.486 0.726 22 140 Sio2 3.686 5.429 0.679 23 120 Sio2 2.663 5.010 0.530 24 140 Al2O3 2.025 7.040 0.287 25 80 Sio2 1.936 3.548 0.545 26 80 Sio2 1.576 3.477 0.453 27 80 Tio2 1.296 3.966 0.326 28 80 CaCo3 0.867 3.878 0.223 29 80 Al2O3 1.008 3.304 0.304 30 80 Cuo 1.309 3.963 0.290 31 80 Cuo 1.517 3.782 0.401 32 120 CaCo3 1.604 6.000 0.267 33 120 Cuo 1.696 5.055 0.335 34 160 Sio2 4.726 5.963 0.792 35 160 Tio2 4.251 6.471 0.653 36 160 CaCo3 3.453 6.547 0.527 37 160 zno 1.914 8.571 0.223 38 160 zno 2.125 7.970 0.266 39 160 Al2O3 2.729 8.312 0.328 40 160 Al2O3 2.822 8.121 0.347 41 160 Cuo 3.564 6.006 0.593 42 160 Sio2 4.897 6.167 0.794 43 160 Tio2 4.019 6.474 0.621 44 140 CaCo3 2.160 5.854 0.368 45 80 zno 1.077 3.974 0.270 Representative cross-sectional images of the weld beads obtained under different flux conditions are shown in Fig. 3. 3- Modeling This section introduces the integrated modeling framework developed to predict weld quality metrics in TIG welding. To begin with, Ridge regression was employed as a straightforward and interpretable approach, providing initial insights into the significance of process parameters and establishing a baseline predictive capability. Ridge regression adds an L2 penalty to ordinary least squares, improving stability under multicollinearity and small datasets. It preserves all parameters for transparency but, as a linear method, cannot fully capture nonlinear thermal–fluid interactions, especially with mixed numerical (welding current) and categorical (flux type) inputs [ 15 ]. Recognizing these limitations, the study advanced to data-driven modeling, selecting XGBoost over other ML techniques such as k-Nearest Neighbors (k-NN) or SVM. Unlike kNN, which relies on proximity in the feature space and is unsuitable for real-time industrial deployment [ 16 ], XGBoost is an ensemble learning algorithm based on decision trees that iteratively builds a strong predictive model by combining many weak learners. At each step, the algorithm minimizes a loss function (e.g., squared error for regression) by fitting new trees to the residuals of the previous model, while applying regularization terms to control model complexity and prevent overfitting. This tree-based boosting framework is highly effective for capturing nonlinearities and interactions between features. XGBoost provides robust predictive performance and is fully compatible with Industry 4.0 applications, enabling real-time process monitoring and adaptive optimization [ 17 ]. Although XGBoost is inherently a “black-box” model, interpretability is achievable through SHAP (SHapley Additive exPlanations) values, allowing identification of the most influential process parameters and providing actionable insights for process control. Given the strong performance of XGBoost, further testing of alternative models such as SVM was deemed unnecessary [ 18 ]. 3 − 1 Data Classification The experimental dataset was partitioned into training (60%), validation (20%), and test (20%) subsets. The training set was used to estimate model parameters, while the validation set enabled hyperparameter tuning and overfitting control, a critical step in welding studies with limited and noisy data. The test set, kept unseen during model development, provided an unbiased measure of generalization. Unlike many prior works that report only training and test performance, this study emphasizes validation analysis as a more realistic indicator of model robustness under experimental uncertainties, supporting a rigorous comparison of Ridge regression and XGBoost. As shown in Fig. 4, the correlation heatmap indicates that the input parameters exhibit no strong associations with one another, with no strong correlations (|r| < 0.3). This absence of multicollinearity confirms that the features contribute independent information, ensuring that the tabular dataset is suitable for regression-based modeling and can provide reliable predictive insights. 3 − 2 Data-Driven Regression Modeling for D/W Ratio Ridge Regression was used as the baseline model for performance evaluation. In its standard form, linear regression estimates the relationship between an output variable y (e.g., weld quality metrics such as D/W ratio) and a set of input variables, px1​,x2​,…,xp​, by minimizing the sum of squared residuals (Eq. 1): $$\:\left({y}_{\widehat{i}}-{y}_{i}\right)\sum\:_{i=1}^{n}{min}_{\beta\:}$$ 1 Variable \(\:{\:y}_{i}\:\) represents the observed value for the i th sample, while \(\:{\:y}_{\widehat{i}}\) ​ denotes the predicted response obtained from the model. The regression coefficients β are the parameters to be estimated, and their magnitudes are constrained by introducing a penalty term. However, when predictors are highly correlated, or when the number of predictors is large relative to the number of observations, OLS solutions become unstable, leading to large and unreliable coefficient estimates [ 19 ]. This instability reduces the generalization ability of the model. Ridge regression modifies the OLS L2-norm penalty on the coefficients (Eq. 2): $$\:\left[{}_{i}{}^{2}\lambda\:\sum\:_{j=1}^{p}\beta\:\:+{\left({y}_{\widehat{i}}-{y}_{i}\right)}^{2}\sum\:_{i=1}^{n}{min}_{\beta\:}\right]$$ 2 Here, λ is the regularization parameter controlling the degree of shrinkage. When 𝜆 = 0, Ridge reduces to OLS. When 𝜆 > 0, large coefficients are penalized, shrinking them toward zero but never eliminating them completely. This shrinkage effect stabilizes the solution, reduces model variance, and improves prediction accuracy on unseen data. Unlike Lasso regression, which can shrink some coefficients exactly to zero (feature selection), Ridge keeps all predictors in the model, making it especially suitable when all process parameters are physically relevant, as is typically the case in welding applications [ 19 ]. The predictive performance of the model was evaluated using RMSE, MAE, and the coefficient of determination (R 2 ), which were calculated using the following formulas (Equations 3–5). $$\:\sqrt{{\left({y}_{\widehat{i}}-{y}_{i}\right)}^{2}\sum\:_{i=1}^{n}\frac{1}{n}}=RSME$$ 3 $$\:\left|{y}_{\widehat{i}}-{y}_{i}\right|\sum\:_{i=1}^{n}\frac{1}{n}=\:MAE$$ 4 $$\:\frac{\sum\:_{i=1}^{n}{\left({y}_{\widehat{i}}-{y}_{i}\right)}^{2}}{\sum\:_{i=1}^{n}{\left(y-{y}_{i}\right)}^{2}}-1={R}^{2}$$ 5 Here, y i ​ and \(\:{y}_{\widehat{i}}\:\) Present the observed and predicted values of the i th sample, respectively, where y​ is the mean of all observed values, and n is the total number of data points. RMSE quantifies the square root of the average squared errors, MAE measures the average absolute deviation, and R 2 indicates the proportion of variance in the observed data explained by the model. Table 3 summarizes the results across training, validation, and testing datasets. Table 3 Performance of Ridge regression models for predicting DOP, WBW, and D/W Ratio on training, validation, and test datasets Target Split RMSE MAE R2 DOP train 0.333806 0.266436 0.868953 DOP val 0.384843 0.310667 0.863411 DOP test 0.43599 0.35949 0.868997 Width train 0.398249 0.287422 0.887385 Width val 0.665855 0.521778 0.83809 Width test 0.524787 0.460592 0.868682 D/W Ratio train 0.063356 0.052564 0.808047 D/W Ratio val 0.081212 0.076175 0.764146 D/W Ratio test 0.07886 0.068706 0.770766 For DOP, Ridge explained ~ 87% of the variance with RMSE 0.33–0.44 mm, showing stable train–validation agreement but leaving some variance unaccounted for. WBW showed R² = 0.83–0.89, with higher validation errors (RMSE = 0.666, MAE = 0.522) than in the test set, indicating moderate sensitivity to data variation and unmodeled interactions. For D/W, explanatory power was lower (R² = 0.764–0.808) despite small absolute errors (RMSE = 0.063–0.079), reflecting compounded variability from both DOP and WBW. To sum up, the model captured the main effects of current and flux, offering a reliable baseline for further refinement. Figure 5 reveals that, based on the test data, the residual analysis showed that for DOP, residuals were centered close to zero (mean = 0.033, SD = 0.434), indicating unbiased predictions but with moderate variability. WBW exhibited a similar near-zero bias (mean = − 0.009, SD = 0.523), though the wider spread suggested less stability. In contrast, the D/W ratio displayed the most precise predictions, with residuals tightly clustered around zero (mean = − 0.002, SD = 0.078). The absence of clear patterns across all plots confirms that the Ridge model maintained stability, even if certain responses involved higher variability. Figure 6 presents the relationships among the predicted weld quality metrics. DOP and WBW showed a relatively strong correlation, as increases in welding current and certain fluxes tended to simultaneously enlarge both parameters. Consequently, fluctuations in one often influenced the other, and this coupling was reflected in the consistently high R² values (> 0.83) across splits. In contrast, the D/W ratio behaved more independently, since it is a derived parameter that balances penetration against width. Its variation was strongly affected by small changes in both DOP and WBW, but neither variable alone could fully determine it, explaining that the D/W ratio resulted in lower validation accuracy (R² = 0.667) despite maintaining very low prediction errors (RMSE = 0.063–0.093). Thus, while DOP and WBW were mutually reinforcing and strongly tied to process conditions, the D/W ratio introduced additional complexity, being less directly influenced by any single parameter and more sensitive to their combined fluctuations. As illustrated in Fig. 7, heatmaps of RMSE, MAE, and R² highlight differences in predictive performance across the three targets. D/W ratio showed the lowest errors (RMSE ≈ 0.07, MAE ≈ 0.06), confirming its stability as a predictive variable. DOP had higher errors (RMSE ≈ 0.38, MAE ≈ 0.30) but the strongest correlation with parameters (R² ≈ 0.87). WBW displayed the largest errors (RMSE up to 0.67, MAE up to 0.52) and weaker explanatory power (R² ≈ 0.86), reflecting its dependence on complex effects such as arc stability and heat distribution. Overall, D/W ratio and DOP emerge as more robust and interpretable responses for TIG welding optimization, while WBW remains less predictable. The Ridge regression model showed moderate predictive performance across the weld quality indicators (Fig. 8). For DOP, the model achieved R² = 0.851, indicating accurate capture of welding current, Flux composition, and molten pool effects. WBW prediction performed best with R² = 0.855, reflecting effective modeling of lateral heat distribution and arc constriction. The D/W Ratio exhibited the lowest absolute prediction errors (mean = − 0.002, SD = 0.078) but a lower R² = 0.743, owing to its compressed dynamic range, where small absolute deviations represent a larger proportion of total variance. 3–3 XGBoost modeling: Due to the limited capability of Ridge regression, it was not sufficient for this study. Therefore, XGBoost was employed as the primary model, offering higher accuracy and robustness in predicting WBG. Hyperparameter tuning was carried out prior to presenting the XGBoost modeling results. As shown in Table 4, the Optuna-based search identified an optimal setup with n_estimators = 194 and learning rate = 0.160, providing fast yet stable convergence. A relatively high tree depth (max_depth = 9) combined with min_child_weight = 3 enabled the model to capture nonlinear dependencies while preventing overfitting. Regularization through sampling (subsample = 0.657, colsample_bytree = 0.633) further enhanced robustness by increasing model diversity. The tuning process was integrated with a K-fold cross-validation strategy, which ensured that the selected parameters generalized well across different subsets of the data. Table 4 Hyperparameters for XGBoost modeling n_estimators learning_rate max_depth min_child_weight subsample colsample_bytree 194 0.160 9 3 0.657 0.633 The comparison of Ridge regression and XGBoost metrics is provided in Table 5. For DOP, XGBoost improved R² from 0.869 to 0.956 with ~ 43% error reduction; for WBW, R² rose from 0.869 to 0.910 with ~ 17% improvement; and for the D/W ratio, R² increased from 0.771 to 0.870 with ~ 25% lower RMSE. These results indicate that while Ridge regression can capture general trends, XGBoost more effectively models nonlinear interactions, delivering superior accuracy and robustness for weld geometry prediction. Table 5 Comparative performance of Ridge regression and XGBoost models for predicting weld geometry responses, including DOP, WBW, and D/W Target R2 (test) RMSE (test) MAE (test) Model DOP 0.868997322 0.435989773 0.359490488 Ridge Width 0.86868184 0.524787275 0.46059194 Ridge D/W Ratio 0.770766489 0.078860262 0.068706048 Ridge DOP 0.955894672 0.25297741 0.204567863 XGB Width 0.910070433 0.434282324 0.340601983 XGB D/W Ratio 0.870027603 0.05938062 0.05101442 XGB As shown in Fig. 9, SHAP summaries for WBW and DOP identify welding current as the dominant factor. Higher currents increase heat input, enhancing penetration, widening the fusion zone, and raising the D/W ratio, while lower currents reduce these responses. Flux composition has a secondary influence: SiO₂ strongly enhances penetration and D/W ratio (D/W up to 0.79), TiO₂ provides balanced performance (D/W ~ 0.6–0.7), and ZnO/Al₂O₃ promotes bead widening (> 8 mm) but lower penetration. 4- Result and discussion This section provides a detailed analysis of the experimental results, focusing on the influence of flux compositional features on WBG. DOP and WBW are employed as the primary metrics for evaluating welding performance, as they jointly capture the balance between penetration capability and lateral heat distribution. DOP is a critical parameter because it reflects the extent of energy transfer into the workpiece and directly determines the load-bearing capacity and structural integrity of the weld. A high DOP indicates efficient utilization of arc energy and ensures sufficient fusion for single-pass welding in medium to thick sections [ 20 , 21 ]. In contrast, WBW represents the degree of lateral spread of the molten pool, which strongly affects arc stability, heat distribution, and dimensional control. In TIG welding, a narrower WBW is generally preferred, as it reduces lateral heat dispersion and helps limit the heat-affected zone (HAZ). A smaller HAZ is beneficial since it minimizes undesirable microstructural transformations, grain coarsening, and the loss of mechanical properties such as hardness and toughness in regions adjacent to the weld [ 22 ]. According to the SHAP analysis (Fig. 9), SiO₂ was identified as the most influential flux on WBG. Experimental results showed that these fluxes increased WBW; however, penetration depth increased more significantly, leading to a marked improvement in the D/W ratio (e.g., from 0.499 to 0.793 for SiO₂) [ 23 ]. This behavior reflects the arc constriction effect, which concentrates energy and drives deeper fusion into the base material. Although the bead became wider, the improved D/W ratio and the confinement of thermal influence into a deeper rather than wider profile effectively helped reduce excessive HAZ growth [ 24 ]. In order to rationalize the observed enhancement in DOP and the concurrent reduction in WBW under specific flux conditions, it is necessary to consider the fundamental transport forces acting within the weld pool. Among these, the Marangoni force, Lorentz (electromagnetic) force, buoyancy force, and aerodynamic drag force play decisive roles, and their relative magnitudes are strongly governed by the welding current, flux material composition, and arc behavior [ 25 ]. A higher DOP generally indicates more efficient energy concentration at the weld root, while WBW reflects the lateral spread of heat and molten metal. Therefore, fluxes that simultaneously promote deeper penetration and restrict excessive bead widening are expected to yield higher D/W ratios. By examining the trends in DOP and WBW for each flux type, a mechanistic understanding can be developed regarding how arc constriction and Marangoni convection collectively govern the final D/W ratio [ 26 ]. For the Marangoni force, the temperature-dependent surface tension gradient plays a central role in directing molten metal flow. Oxygen released from fluxes such as SiO₂ reverses the temperature coefficient of surface tension (dσ/dT < 0), inducing inward-directed surface flow. This reverse Marangoni convection channels heat and molten metal toward the weld root, producing deeper penetration and limiting bead spreading [ 27 ]. The strong D/W ratio achieved with SiO₂ at 160 A (0.794, + 46% compared to 0.545 at 80 A) is directly attributable to this mechanism. By contrast, fluxes with slower oxygen release, such as TiO₂ (0.653 at 160 A, + 100% improvement from 0.326 at 80 A) or those with low oxygen activity, like Al₂O₃ (0.347 at 160 A, only + 14% compared to 0.304 at 80 A), generate weaker Marangoni reversal, resulting in shallower and wider bead profiles. The Lorentz force further reinforces penetration at elevated welding currents. As current increases, or when the arc is constricted by oxygen-rich fluxes, the local current density and self-induced magnetic field intensify. This electromagnetic body force drives molten metal downward and inward, enhancing DOP [ 28 ]. As observed, SiO₂ showed a DOP increase from 1.58 mm at 80 A to 4.90mm at 160 A (+ 210%), while TiO₂ improved even more dramatically from .30 mm to 4.25 mm (+ 228%), confirming the dominance of Lorentz forces under high-current and oxygen-active flux conditionsAlthough both TiO₂ and SiO₂ are oxygen-rich oxides, SiO₂ proves more effective in supplying active oxygen to the weld pool because its superiority depends not only on stoichiometric oxygen content but also on its thermodynamic stability, decomposition kinetics, and oxygen chemical activity [ 29 ]. SiO₂ has a relatively lower Gibbs free energy of oxygen release in the arc temperature range, which promotes gradual and sustained liberation of oxygen ions. This controlled release stabilizes the arc plasma and ensures a steady reversal of Marangoni convection [ 30 ]. In contrast, TiO₂ tends to release oxygen less efficiently due to its higher decomposition temperature and its strong affinity for oxygen, forming stable sub-oxides such as Ti₂O₃ that “trap” oxygen [ 31 ]. Consequently, despite similar nominal oxygen contents, SiO₂ delivers a higher effective oxygen activity to the weld pool, producing stronger arc constriction and more consistent inward molten flow [ 32 ]. This clarifies why, under the same welding currents, SiO₂ consistently yielded the highest D/W ratio (0.794 at 160 A) compared to TiO₂ (0.653 at 160 A). The buoyancy force, arising from thermal expansion (∝ gβΔT), tends to spread heat laterally and widen the bead in conventional TIG welding. However, in the presence of strong reverse Marangoni and Lorentz forces, buoyancy acts more as a secondary stabilizing effect, reinforcing downward flow [ 33 ]. This finding demonstrates that CaCO₃, despite its limited Marangoni activity, showed a substantial DOP increase from 0.87 mm at 80 A to 3.45 mm at 160 A (+ 298%), yet the corresponding D/W ratio remained moderate (0.527 at 160 A). Finally, the aerodynamic drag force, exerted by the plasma jet, plays a complementary role. When the arc is constricted, the plasma velocity and axial pressure increase, forcing molten metal toward the centerline. This aerodynamic drag complements Marangoni reversal and J×B forcing, narrowing the bead and deepening penetration [ 34 ]. However, in fluxes with unstable vaporization, such as ZnO, arc instability reduced this beneficial effect, leading to shallow penetration (1.08 → 1.91 mm, + 77%) and wider beads (3.97 → 8.57 mm, + 116%), which in turn decreased the D/W ratio from 0.270 at 80 A to just 0.223 at 160 A (− 18%). The welding. Across all fluxes, an increase in current from 80 A to 160 A substantially improved penetration; however, the net D/W ratio improvement depended on the balance between DOP gain and WBW widening [ 35 ]. For SiO₂, the most effective flux, the DOP increased from 1.58 mm at 80 A to 4.90 mm at 160 A, corresponding to a 210% improvement. WBW expanded moderately from 3.55 mm to 6.17 mm (74% increase), yielding a final D/W ratio of 0.79 at 160 A compared to 0.545 at 80 A (46% enhancement). As summarized in Table 6, flux composition and welding current strongly affect weld geometry, with SiO₂ providing the highest D/W ratio (0.794 at 160 A) via stable Marangoni flow, while other fluxes show varying efficiency, highlighting the key role of oxygen-release kinetics. Table 6 Comparison of DOP, WBW, and D/W ratio across welding currents (80 → 160 A) for different Flux DOP (mm) 80A → 160A Bead Width (mm) 80A → 160A D/W 80A → 160A SiO₂ 1.76 → 4.81 3.51 → 6.07 0.499 → 0.793 TiO₂ 1.30 → 4.25 3.97 → 6.47 0.326 → 0.653 CaCO₃ 0.87 → 3.45 3.88 → 6.55 0.223 → 0.527 CuO 1.41 → 3.56 3.87 → 6.01 0.346 → 0.593 Al₂O₃ 1.01 → 2.78 3.30 → 8.22 0.304 → 0.338 ZnO 1.08 → 2.02 3.97 → 8.27 0.270 → 0.245 4 − 1 Uncertainty Estimation Performance In predictive modeling, UQ provides insight into the confidence of model outputs. Even when models achieve high accuracy, their predictions are not deterministic and carry associated uncertainty [ 36 ]. Two principal classes of uncertainty are typically distinguished. The first is aleatoric uncertainty, also referred to as data uncertainty, which arises from inherent variability or noise in the observed data. In welding and WAAM processes, aleatoric uncertainty is linked to uncontrollable micro-scale fluctuations such as melt pool turbulence, local arc instabilities, and measurement errors. Importantly, this type of uncertainty cannot be reduced simply by acquiring more data, as it reflects true randomness in the process. The second class is epistemic uncertainty, or model uncertainty, which results from incomplete knowledge of the underlying system or insufficient data to fully train the model. For instance, using a limited dataset or an inadequate model architecture introduces epistemic uncertainty. Unlike aleatoric uncertainty, epistemic uncertainty can be reduced through improved modeling strategies, additional data collection, or more expressive algorithms. Some frameworks additionally distinguish between optimistic and pessimistic uncertainty estimates, which reflect whether PIs underestimate or overestimate the true variability [ 37 , 38 ]. In the present work, uncertainty was quantified using quantile regression with XGBoost. Unlike conventional regression, which predicts the conditional mean, quantile regression estimates conditional quantiles of the response distribution, such as the 5th, 50th, and 95th percentiles. This allows direct estimation of PIs. For each target, models were trained to predict the lower bound (5th quantile), the median (50th quantile), and the upper bound (95th quantile). The interval between the 5th and 95th quantile provides a 90% PIs, which captures the variability in process outcomes [ 39 ]. This approach directly addresses aleatoric uncertainty, since the width of the interval reflects inherent data variability. Three XGBoost quantile models (0.05, 0.50, 0.95) were trained and optimized with pinball loss, yielding 90% PIs. On the independent test set (n = 9), coverage was 66.7% for DOP, 77.8% for WBW, and 77.8% for D/W ratio, with normalized widths of ~ 40–44%. WBW performed best (R² = 0.9242, RMSE = 0.3774), DOP showed a strong fit (R² = 0.8955) but poor coverage, and the D/W ratio had the lowest R² (0.8080), though a reasonable interval width (39.95%). Interval width correlated with prediction error (r = 0.5881), validating its role as an uncertainty indicator. The quantile regression framework extends beyond deterministic point predictions by explicitly establishing confidence bounds for model outputs. From a manufacturing perspective, this approach enables risk-informed decision-making, predictive quality assurance, and paves the way toward digital twin integration in Industry 4.0 welding environments [ 40 ]. Coverage results (Table 7) show that the 90% PIs from quantile regression are under-dispersed for DOP (66.67% coverage) and better, but still short of nominal, for WBW and D/W Ratio (77.78% each). Although normalized interval widths are similar across targets (~ 40–44%), DOP's lower coverage indicates its predictive uncertainty is underestimated, likely owing to higher intrinsic variability or unmodeled nonlinear effects. Point-prediction metrics support this: WBW has the strongest performance (R² = 0.9242, RMSE = 0.3774) and the most reliable intervals; DOP shows a high R² (0.8955) but moderate RMSE and poor coverage, implying extreme errors are underrepresented; D/W Ratio has the lowest R² (0.8080) yet reasonably narrow intervals (39.95% normalized width), warranting cautious interpretation. The positive correlation between interval width and absolute prediction error (r = 0.5881) confirms that wider intervals meaningfully reflect larger uncertainty, providing a valuable reliability indicator for model predictions. This correlation demonstrates that the quantile regression framework successfully captures the relationship between prediction uncertainty and error magnitude. Practically, WBW predictions are the most ready for industrial use, while DOP requires additional data or recalibration (or more conservative control margins); D/W Ratio predictions remain useful but should be treated with caution due to their compressed dynamic range. From a manufacturing perspective, this uncertainty-aware approach enables risk-informed decision-making and predictive quality assurance by identifying when predictions have higher uncertainty, paving the way toward more reliable welding process optimization in Industry 4.0 applications. Table 7 UQ Performance Metrics of the XGBoost Median-Quantile Model on the Test Set. Target Coverage (%) Avg Interval Width Normalized Width (%) RMSE R² DOP 55.55556 1.716195 44.47253 0.367877 0.906732 Width 77.77778 2.390357 45.38365 0.440114 0.907639 D/W Ratio 66.66667 0.219501 38.5766 0.068579 0.826643 Figures 10–12 present the UQ analysis for DOP, WBW, and D/W Ratio, each evaluated with 90% PIs. For DOP (Fig. 10), only 55.6% of test samples fell within the PIs, revealing strong under-coverage compared to the nominal 90%. Interval widths ranged from 1.0 to 3.2, with a mean of 1.716, and four samples (0, 2, 6, 8) lay outside the bounds. While intermediate widths (1.5–2.0) achieved full coverage, both very narrow and very wide intervals failed, indicating systematic underestimation of variability. For WBW (Fig. 11), coverage improved to 77.8%, though still below the nominal level. Interval widths were relatively consistent, ranging from 1.75 to 2.75 with a mean of 2.390, producing sharp yet under-dispersed intervals. Calibration analysis revealed fluctuations, with some bins achieving full coverage and others none at all, emphasizing the need for recalibration despite the strong point-prediction accuracy (R² = 0.9242). For the D/W Ratio (Fig. 12), coverage again reached only 66.7%, with three of nine samples, particularly higher ratio cases, lying outside the intervals. Widths averaged 0.220, predominantly concentrated around 0.25–0.27, where coverage reached 100%, while narrower intervals (~ 0.18–0.20) consistently failed. This imbalance highlights that the model tended to underestimate variability for smaller widths, resulting in inconsistent reliability. All three models retained strong predictive capability after integrating UQ. For D/W ratio, the model achieved an R² of 0.8080 with an RMSE of 0.0677, confirming reliable point estimates alongside informative intervals. Normalized interval widths were consistent across targets (≈ 40–44%), indicating stable relative uncertainty irrespective of the output variable. However, coverage rates (55.6–77.8%) revealed systematic under-coverage, with DOP performing worst (55.6%), followed by D/W ratio (66.7%) and WBW (77.8%). This underestimation stems from the stochastic multiphysics of TIG welding, transient fluid flow, heat transfer, and phase transformations, and the limited dataset size (n = 36), which constrains generalization in extreme conditions. Despite these limitations, the stable interval widths suggest that the framework captured genuine process variability rather than output-specific artifacts. Furthermore, positive correlations between interval width and prediction error (0.20–0.65) confirm that the intervals provide meaningful reliability information. In practice, narrow intervals can guide automated control and real-time parameter tuning, whereas wide intervals should trigger manual inspection or adaptive strategies, enabling risk-informed quality assurance. Conclusion This study demonstrated the integration of systematic A-TIG welding experiments with ML and UQ for WBG prediction. Among the tested fluxes, SiO₂ produced the most favorable welds, achieving the highest D/W ratio of 0.794 at 160 A, while TiO₂ and CuO offered moderate improvements, and ZnO performed poorly. Ridge regression provided a stable linear baseline, but XGBoost more effectively captured nonlinear interactions, reducing predictive errors by approximately 20–40%. UQ, through quantile regression, enabled the generation of 90% PIs, with empirical coverage ranging from 55.6–77.8% across responses. The lowest coverage was observed for depth of penetration (55.6%), followed by D/W ratio (66.7%) and WBW (77.8%). Although the intervals underestimated variability, their normalized widths remained consistent at ≈ 40–44% of the target domain, and they were positively correlated with prediction errors, confirming their value as indicators of predictive reliability. Producing the highest D/W = 0.794, SiO₂ had the highest DOP altered from 1.58 → 4.90 mm (+ 210%) and WBW from 3.55 → 6.17 mm (+ 74%). Raising current from 80 → 160 A consistently increased penetration for all fluxes, but only SiO₂ and TiO₂ converted this into high D/W ratios because their oxygen release sustained inward flow; others mainly widened the bead. Ridge regression explained 76–87% of R² with RMSE up to 0.66 mm, serving as a linear baseline. XGBoost outperformed it with R² = 0.956 (DOP), 0.910 (WBW), 0.870 (D/W), and RMSE reduced to 0.25–0.43 mm, i.e., 20–40% lower errors, by capturing nonlinear effects of flux type and current. Welding current was the dominant factor; flux type came second. SiO₂ contributed the most to penetration and D/W, while ZnO widened the bead without penetration benefits. Quantile regression gave 90% PIs with coverage 55.6% (DOP), 77.8% (WBW), 66.7% (D/W), and normalized interval widths ≈ 40–44%. Under-coverage shows underestimation of variability, but the positive correlation (r ≈ 0.59) between interval width and error proves the intervals are informative. Declarations Acknowledgment The authors sincerely thank the Faculty of Engineering at Ferdowsi University for their generous support in granting access to the necessary facilities and laboratories for this research. They also extend their deep appreciation to the anonymous reviewers for their thoughtful feedback and constructive suggestions, which have significantly contributed to improving the quality of this work. Funding No funding was obtained for this study. Declaration of conflicting interests The authors did not receive support from any organization for the submitted work. Ethics approval and consent to participate and publication This study was conducted in accordance with the ethical guidelines outlined by the Committee on Publication Ethics (COPE). All participants provided written informed consent to participate in the study . Declaration of generative AI and AI-assisted technologies in the manuscript preparation process In the preparation of this manuscript, the authors utilized AI-assisted tools (DeepSeek and ChatGPT) to enhance writing clarity and coherence. Following AI assistance, the authors critically reviewed, revised, and validated the content, assuming full responsibility for all aspects of the published work. CRediT Author Statement Mahdi Mazloom Farsibaf : Conceptualization, Methodology, Software, Investigation, Data Curation, Writing – Original Draft, Writing – Review & Editing, Visualization. Seyed Moein Fareghi : Investigation, Validation. Kiana Arteshyar: Writing – Original Draft, Writing – Review & Editing. Kiarash Rahimi: Methodology, Writing – Original Draft. Dr. Farhad Kolahan: Supervision, Project Administration, Resources, Writing – Review & Editing. 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Adv Neural Inf Process Syst 34:10971–10984. https://doi.org/10.48550/arXiv.2011.09588 Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 11 May, 2026 Reviewers invited by journal 06 May, 2026 Editor invited by journal 01 May, 2026 Editor assigned by journal 28 Apr, 2026 First submitted to journal 26 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9530256","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":635546086,"identity":"b3c54599-2fac-459e-aa7b-2d15d4bac950","order_by":0,"name":"Mahdi Mazloom Farsibaf","email":"","orcid":"","institution":"Ferdowsi University of Mashhad","correspondingAuthor":false,"prefix":"","firstName":"Mahdi","middleName":"Mazloom","lastName":"Farsibaf","suffix":""},{"id":635546087,"identity":"30727dbb-06c2-4f20-b5bb-72e622a40c3a","order_by":1,"name":"Seyed Moein Fareghi","email":"","orcid":"","institution":"Ferdowsi University of 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setup\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-9530256/v1/3d5fdd11ab665128cd6cde13.png"},{"id":109405828,"identity":"6ca18d9f-fcab-4bed-9306-fe0c5ac4e289","added_by":"auto","created_at":"2026-05-17 13:20:21","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":2741398,"visible":true,"origin":"","legend":"\u003cp\u003eCross-sectional weld profiles obtained according to the experimental matrix\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-9530256/v1/773a9049551685ca0028d0ec.jpeg"},{"id":109376497,"identity":"bb486fc0-d897-456f-8e11-4fc7d606a31c","added_by":"auto","created_at":"2026-05-16 14:56:54","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":212058,"visible":true,"origin":"","legend":"\u003cp\u003eInput feature correlation heatmap for welding current and flux categories\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-9530256/v1/066b85c5547fd26c11af52d2.png"},{"id":109376502,"identity":"0f5e7ee9-d666-497f-9dae-542fe4bb7f27","added_by":"auto","created_at":"2026-05-16 14:56:54","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":68168,"visible":true,"origin":"","legend":"\u003cp\u003eResidual analysis of the Ridge regression model for DOP, WBW, and D/W ratio\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-9530256/v1/4ab4bc24ef6c7f1e678607d3.png"},{"id":109405590,"identity":"eae64cc8-0de9-43d2-9a8e-6b79bb6aadde","added_by":"auto","created_at":"2026-05-17 13:19:17","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":167541,"visible":true,"origin":"","legend":"\u003cp\u003eHeatmap analysis of Ridge regression model performance across training, validation, and test datasets\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-9530256/v1/e8546b463bff5618645cb5db.png"},{"id":109405591,"identity":"9b06cdba-1fb1-4f95-b1a8-ba937b55fb0b","added_by":"auto","created_at":"2026-05-17 13:19:17","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":212970,"visible":true,"origin":"","legend":"\u003cp\u003ePerformance evaluation of the Ridge model across different weld quality targets and dataset splits\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-9530256/v1/e6e80db09e1b2399f568c98d.png"},{"id":109376498,"identity":"042de4e3-d7f2-4cd6-967a-7a87bcca61e9","added_by":"auto","created_at":"2026-05-16 14:56:54","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":108032,"visible":true,"origin":"","legend":"\u003cp\u003ePredictive performance of the Ridge regression model for three weld quality indicators based on test data\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-9530256/v1/61b06bbd991afea8ef507dce.png"},{"id":109405734,"identity":"e5ebfbc4-a7cd-45f7-a0e3-373fcd3e0ab7","added_by":"auto","created_at":"2026-05-17 13:20:00","extension":"jpeg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":176522,"visible":true,"origin":"","legend":"\u003cp\u003eSHAP summary plots for the contributions of welding current and Flux composition to D/W ratio, DOP, and WBW in TIG welding\u003c/p\u003e","description":"","filename":"floatimage9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-9530256/v1/21cb3b331e62d0ea10f9a6fe.jpeg"},{"id":109405749,"identity":"816d5f54-25f3-43c2-9cda-22b55bbc8d6c","added_by":"auto","created_at":"2026-05-17 13:20:02","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":347649,"visible":true,"origin":"","legend":"\u003cp\u003eUQ analysis for DOP\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-9530256/v1/47cc000d6684becb68ba8bec.png"},{"id":109405807,"identity":"3c82d432-97ab-4bb0-8197-c0c2c1b14eb6","added_by":"auto","created_at":"2026-05-17 13:20:14","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":357979,"visible":true,"origin":"","legend":"\u003cp\u003eUQ analysis for weld WBW\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-9530256/v1/028b5484d5f79c4ca8ce1a54.png"},{"id":109376504,"identity":"26c7ac4d-7b22-41c5-96c0-5506646ddbaf","added_by":"auto","created_at":"2026-05-16 14:56:54","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":371148,"visible":true,"origin":"","legend":"\u003cp\u003eUQ analysis for D/W ratio prediction\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-9530256/v1/7559dd96d8f8817742df2cad.png"},{"id":109406250,"identity":"eb794b8a-3ee1-45ef-93d7-aedff0c5793d","added_by":"auto","created_at":"2026-05-17 13:27:16","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6189517,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9530256/v1/fb3dcab2-919d-440b-b4e0-162bbe29d8a1.pdf"}],"financialInterests":"","formattedTitle":"Machine Learning and Uncertainty Quantification for Predicting Weld Bead Geometry of AISI 304L in Micro-Size A-TIG Welding","fulltext":[{"header":"1- Introduction","content":"\u003cp\u003eTungsten Inert Gas (TIG) is widely used for high-quality, defect-sensitive joints because it produces a controllable, stable weld pool using a non-consumable tungsten electrode and an inert shielding gas [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. The TIG welding process is widely used in industries such as aerospace, petrochemical, and medical equipment manufacturing due to its high precision and excellent surface quality [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. It is also commonly applied for welding thin metals and special alloys like aluminum in the automotive and food industries [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. However, conventional TIG has practical limitations for thicker sections: single-pass penetration is shallow (typically\u0026thinsp;\u0026asymp;\u0026thinsp;2\u0026ndash;3 mm), deposition rates are low, edge preparation requirements are strict, and travel speeds are relatively slow, limiting the degree of welding automation and making multi-pass welding necessary for many structural applications [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. These constraints increase cycle time and cost when welding medium-to-thick components [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Several alternative and hybrid approaches have been introduced to address the inherent limitations of TIG welding. Techniques such as laser and electron-beam welding offer deep penetration at high travel speeds, while hybrid methods such as laser-arc and ultrasonic-assisted TIG merge energy sources or additional forces to enhance penetration, minimize the heat-affected zone (HAZ), and improve overall productivity. Such methods can address specific industrial needs but often require specialized equipment or present new process-control challenges that complicate adoption in standard shop floors.\u003c/p\u003e \u003cp\u003eActivated TIG (A-TIG) offers a practical, low-cost route to deeper single-pass penetration by applying activating fluxes (e.g., TiO₂, SiO₂, Fe₂O₃) to the workpiece prior to welding [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. These fluxes promote arc constriction, alter surface-tension gradients (reversing Marangoni flow), and increase current density at the arc root, collectively concentrating heat toward the joint center and producing deeper, narrower welds with reduced HAZ and distortion [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Several experimental and optimization studies have characterized A-TIG performance and flux effects. Singh and Khanna [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] reviewed process fundamentals and reported large penetration gains; Rana et al. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] demonstrated significant penetration and mechanical-property improvements across different flux chemistries and TIG variants. These studies demonstrate that flux chemistry and process parameters significantly influence weld geometry. However, most previous research relies on traditional regression techniques (such as ANOVA), focusing primarily on nano-flux formulations or isolated parameter variations, rather than employing comprehensive, systematic predictive modeling that spans across both Flux composition and process parameters. In recent years, ML has increasingly been applied to welding research for predicting bead geometry, penetration depth, and mechanical properties. Common approaches include artificial neural networks (ANNs), support vector machines (SVM), and genetic algorithms (GA), which have demonstrated improved predictive accuracy over traditional regression methods [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. However, these models are often treated as black boxes, limiting interpretability, and they rarely account for nonlinear parameter interactions in a systematic way. Furthermore, most ML applications in welding focus on macro-process optimization or defect detection, with relatively few studies targeting the D/W ratio that directly governs penetration efficiency [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAt the same time, incorporating UQ into ML frameworks has become increasingly important for welding applications. Unlike conventional predictive models that yield only deterministic point estimates, UQ-enabled methods such as Monte Carlo simulation, Bayesian inference, and quantile regression provide probabilistic outputs with confidence intervals [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. This additional layer of information is critical for handling the inherent variability of processes like A-TIG welding, where arc instabilities and thermofluidic fluctuations can significantly affect penetration behavior. Much of the recent literature has emphasized nano-sized fluxes because of their high surface area and reactivity; however, nano-fluxes can pose handling, dispersion, and scalability issues in practice, motivating investigation of micro-sized alternatives [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. The present study addresses these gaps by experimentally evaluating six micro-structured activating fluxes (SiO₂, TiO₂, Al₂O₃, ZnO, CuO, CaCO₃) in A-TIG welding of SS304 L. A structured full-factorial design, augmented with additional tests for broader coverage, was employed for a total of 45 experimental runs to examine the effects of welding current and flux type. Additionally, data-driven predictive models for weld geometry, including DOP, WBW, and the D/W ratio, were developed. Ridge regression was utilized as an interpretable linear baseline, while XGBoost was applied to capture nonlinear interactions. To enhance decision-making, UQ through quantile regression was incorporated, providing probabilistic PIs for risk-aware choices. To our knowledge, this study is among the first to combine A-TIG experimentation with micro-sized fluxes, explicit machine learning-based prediction, and UQ, specifically focused on the practical D/W metric.\u003c/p\u003e"},{"header":"2- Materials and methods","content":"\u003cp\u003eIn this investigation, SS304L austenitic stainless steel was chosen as the base material due to its wide availability, corrosion resistance, weldability, and mechanical robustness. These characteristics, together with ready availability and ease of fabrication, make this alloy an appropriate base material for assessing the effects of activating fluxes on bead morphology and penetration [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The material\u0026rsquo;s chemical composition and mechanical properties are listed in Fig.\u0026nbsp;1.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTest specimens (100 mm \u0026times; 50 mm \u0026times; 5 mm) were welded using a bead-on-plate method without filler material on a Gam Electric PSQ250 AC/DC welding machine, as depicted in Fig.\u0026nbsp;2. The torch travel speed was kept constant to investigate the effects of welding current and flux composition.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA paste-like mixture was prepared using micro-sized flux powders (nominal 25\u0026ndash;30 \u0026micro;m) and methanol at 0.2 g\u0026middot;mL⁻\u0026sup1; and magnetically stirring the suspension at 600 rpm for 40 min at room temperature (\u0026asymp;\u0026thinsp;25\u0026deg;C), followed by a 3-minute settling period. Representative powder samples were selected at random, and their particle-size distributions were confirmed by particle analysis, validating the nominal 25\u0026ndash;30 \u0026micro;m range reported for the powders by the manufacturer. The flux paste was brushed onto a masked 100 \u0026times; 10 mm area, which was defined using two strips of adhesive tape, and applied to a uniform thickness of 0.2 mm, measured with a filler gauge. The experimental input parameters are summarized in Table\u0026nbsp;1.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTIG input parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWelding Parameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003evalue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElectrode\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThoriated Tungsten 2.4 mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGas Flow Rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10 L.min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (99.9% Argon)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTorch Travel speed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e145 mm/min\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCurrent\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e80,100,120,140,160 A\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eArc length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3 mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAfter completing the welding process, the specimens were sectioned transversely to prepare cross-sectional samples for metallographic examination. Cross-sectional Specimens were prepared according to ASTM E3. Cross-sectional images were captured with an OLYMPUS-530 optical microscope at 200\u0026times; magnification, and DOP and WBW were measured using ImageJ. The welds were visually defect-free, consistent with ISO 17637 visual testing acceptance criteria. The screening test determined the highest and lowest effective currents that impact DOP and WBW in A-TIG welding, guiding subsequent detailed experiments. Experimental A-TIG studies report large sensitivity of penetration and bead shape to both Flux composition and process settings.\u003c/p\u003e \u003cp\u003eThen, a structured experimental matrix was conducted to quantify how activating flux chemistry and welding current affect A-TIG weld geometry. The study began with a screening test: an initial full-factorial matrix (30 runs) was executed in JMP v18.0.1 to map main effects and two-way interactions between factors. To minimize systematic bias, the experimental runs were performed in a randomized order. The matrix was then augmented by 15 additional random runs (total n\u0026thinsp;=\u0026thinsp;45) to enrich sampling near design boundaries, include intermediate current conditions and selected replicates, and provide greater data density for machine-learning training and UQ. The final full-factorial matrix (factors, levels, and measured responses: DOP, WBW, and D/W ratio) is summarized in Table\u0026nbsp;2.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCustom experimental design matrix and corresponding measured outputs\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTest number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCurrent (I)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFlux type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDOP (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eWBW (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eD/W ratio\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.558\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.316\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.592\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.883\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.435\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCaCo3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.474\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.293\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCaCo3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.673\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.287\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.316\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAl2O3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.910\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.219\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.948\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.426\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.313\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.451\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ezno\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.779\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.743\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.263\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ezno\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.258\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.556\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.276\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAl2O3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.587\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.187\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.305\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAl2O3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.714\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.308\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.234\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCuo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.736\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.398\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCaCo3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.895\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.574\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.288\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.321\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.526\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.512\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.105\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.491\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCuo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.594\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.070\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.427\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAl2O3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.725\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.375\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCuo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.787\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.259\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.419\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ezno\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.502\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.835\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.257\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.574\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.302\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.365\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.988\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.486\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.726\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.686\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.429\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.679\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.663\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.530\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAl2O3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.025\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.287\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.936\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.548\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.545\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.576\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.477\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.453\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.296\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.966\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.326\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCaCo3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.867\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.878\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.223\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAl2O3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.304\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.304\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCuo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.309\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.963\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.290\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCuo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.517\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.782\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.401\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCaCo3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.604\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.267\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCuo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.696\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.055\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.335\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.726\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.963\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.792\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.251\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.471\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.653\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCaCo3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.453\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.547\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.527\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ezno\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.914\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.571\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.223\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ezno\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.970\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.266\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAl2O3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.729\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.312\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.328\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAl2O3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.822\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.121\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.347\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCuo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.564\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.593\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.897\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.794\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTio2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.474\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.621\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCaCo3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.854\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.368\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ezno\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.974\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.270\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eRepresentative cross-sectional images of the weld beads obtained under different flux conditions are shown in Fig.\u0026nbsp;3.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3- Modeling","content":"\u003cp\u003eThis section introduces the integrated modeling framework developed to predict weld quality metrics in TIG welding. To begin with, Ridge regression was employed as a straightforward and interpretable approach, providing initial insights into the significance of process parameters and establishing a baseline predictive capability. Ridge regression adds an L2 penalty to ordinary least squares, improving stability under multicollinearity and small datasets. It preserves all parameters for transparency but, as a linear method, cannot fully capture nonlinear thermal\u0026ndash;fluid interactions, especially with mixed numerical (welding current) and categorical (flux type) inputs [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Recognizing these limitations, the study advanced to data-driven modeling, selecting XGBoost over other ML techniques such as k-Nearest Neighbors (k-NN) or SVM. Unlike kNN, which relies on proximity in the feature space and is unsuitable for real-time industrial deployment [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], XGBoost is an ensemble learning algorithm based on decision trees that iteratively builds a strong predictive model by combining many weak learners. At each step, the algorithm minimizes a loss function (e.g., squared error for regression) by fitting new trees to the residuals of the previous model, while applying regularization terms to control model complexity and prevent overfitting. This tree-based boosting framework is highly effective for capturing nonlinearities and interactions between features. XGBoost provides robust predictive performance and is fully compatible with Industry 4.0 applications, enabling real-time process monitoring and adaptive optimization [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Although XGBoost is inherently a \u0026ldquo;black-box\u0026rdquo; model, interpretability is achievable through SHAP (SHapley Additive exPlanations) values, allowing identification of the most influential process parameters and providing actionable insights for process control. Given the strong performance of XGBoost, further testing of alternative models such as SVM was deemed unnecessary [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003e3 − 1 Data Classification\u003c/h3\u003e\n\u003cp\u003eThe experimental dataset was partitioned into training (60%), validation (20%), and test (20%) subsets. The training set was used to estimate model parameters, while the validation set enabled hyperparameter tuning and overfitting control, a critical step in welding studies with limited and noisy data. The test set, kept unseen during model development, provided an unbiased measure of generalization. Unlike many prior works that report only training and test performance, this study emphasizes validation analysis as a more realistic indicator of model robustness under experimental uncertainties, supporting a rigorous comparison of Ridge regression and XGBoost.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;4, the correlation heatmap indicates that the input parameters exhibit no strong associations with one another, with no strong correlations (|r| \u0026lt; 0.3). This absence of multicollinearity confirms that the features contribute independent information, ensuring that the tabular dataset is suitable for regression-based modeling and can provide reliable predictive insights.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003e3 − 2 Data-Driven Regression Modeling for D/W Ratio\u003c/h3\u003e\n\u003cp\u003eRidge Regression was used as the baseline model for performance evaluation. In its standard form, linear regression estimates the relationship between an output variable y (e.g., weld quality metrics such as D/W ratio) and a set of input variables, px1​,x2​,\u0026hellip;,xp​, by minimizing the sum of squared residuals (Eq.\u0026nbsp;1):\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\left({y}_{\\widehat{i}}-{y}_{i}\\right)\\sum\\:_{i=1}^{n}{min}_{\\beta\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eVariable\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:y}_{i}\\:\\)\u003c/span\u003e\u003c/span\u003erepresents the observed value for the i\u003csup\u003eth\u003c/sup\u003e sample, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:y}_{\\widehat{i}}\\)\u003c/span\u003e\u003c/span\u003e​ denotes the predicted response obtained from the model. The regression coefficients β are the parameters to be estimated, and their magnitudes are constrained by introducing a penalty term.\u003c/p\u003e \u003cp\u003eHowever, when predictors are highly correlated, or when the number of predictors is large relative to the number of observations, OLS solutions become unstable, leading to large and unreliable coefficient estimates [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. This instability reduces the generalization ability of the model. Ridge regression modifies the OLS L2-norm penalty on the coefficients (Eq.\u0026nbsp;2):\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\left[{}_{i}{}^{2}\\lambda\\:\\sum\\:_{j=1}^{p}\\beta\\:\\:+{\\left({y}_{\\widehat{i}}-{y}_{i}\\right)}^{2}\\sum\\:_{i=1}^{n}{min}_{\\beta\\:}\\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, λ is the regularization parameter controlling the degree of shrinkage. When \u0026#120582; = 0, Ridge reduces to OLS. When \u0026#120582; \u0026gt; 0, large coefficients are penalized, shrinking them toward zero but never eliminating them completely. This shrinkage effect stabilizes the solution, reduces model variance, and improves prediction accuracy on unseen data. Unlike Lasso regression, which can shrink some coefficients exactly to zero (feature selection), Ridge keeps all predictors in the model, making it especially suitable when all process parameters are physically relevant, as is typically the case in welding applications [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The predictive performance of the model was evaluated using RMSE, MAE, and the coefficient of determination (R\u003csup\u003e2\u003c/sup\u003e), which were calculated using the following formulas (Equations 3\u0026ndash;5).\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:\\sqrt{{\\left({y}_{\\widehat{i}}-{y}_{i}\\right)}^{2}\\sum\\:_{i=1}^{n}\\frac{1}{n}}=RSME$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:\\left|{y}_{\\widehat{i}}-{y}_{i}\\right|\\sum\\:_{i=1}^{n}\\frac{1}{n}=\\:MAE$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:\\frac{\\sum\\:_{i=1}^{n}{\\left({y}_{\\widehat{i}}-{y}_{i}\\right)}^{2}}{\\sum\\:_{i=1}^{n}{\\left(y-{y}_{i}\\right)}^{2}}-1={R}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, y\u003csub\u003ei\u003c/sub\u003e​ and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{\\widehat{i}}\\:\\)\u003c/span\u003e\u003c/span\u003ePresent the observed and predicted values of the i\u003csub\u003eth\u003c/sub\u003e sample, respectively, where y​ is the mean of all observed values, and n is the total number of data points. RMSE quantifies the square root of the average squared errors, MAE measures the average absolute deviation, and R\u003csup\u003e2\u003c/sup\u003e indicates the proportion of variance in the observed data explained by the model. Table\u0026nbsp;3 summarizes the results across training, validation, and testing datasets.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePerformance of Ridge regression models for predicting DOP, WBW, and D/W Ratio on training, validation, and test datasets\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTarget\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSplit\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR2\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDOP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003etrain\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.333806\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.266436\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.868953\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDOP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eval\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.384843\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.310667\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.863411\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDOP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003etest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.43599\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.35949\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.868997\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWidth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003etrain\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.398249\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.287422\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.887385\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWidth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eval\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.665855\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.521778\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.83809\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWidth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003etest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.524787\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.460592\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.868682\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD/W\u003c/p\u003e \u003cp\u003eRatio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003etrain\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.063356\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.052564\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.808047\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD/W\u003c/p\u003e \u003cp\u003eRatio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eval\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.081212\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.076175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.764146\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD/W\u003c/p\u003e \u003cp\u003eRatio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003etest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.07886\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.068706\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.770766\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFor DOP, Ridge explained\u0026thinsp;~\u0026thinsp;87% of the variance with RMSE 0.33\u0026ndash;0.44 mm, showing stable train\u0026ndash;validation agreement but leaving some variance unaccounted for. WBW showed R\u0026sup2; = 0.83\u0026ndash;0.89, with higher validation errors (RMSE\u0026thinsp;=\u0026thinsp;0.666, MAE\u0026thinsp;=\u0026thinsp;0.522) than in the test set, indicating moderate sensitivity to data variation and unmodeled interactions. For D/W, explanatory power was lower (R\u0026sup2; = 0.764\u0026ndash;0.808) despite small absolute errors (RMSE\u0026thinsp;=\u0026thinsp;0.063\u0026ndash;0.079), reflecting compounded variability from both DOP and WBW. To sum up, the model captured the main effects of current and flux, offering a reliable baseline for further refinement.\u003c/p\u003e \u003cp\u003eFigure 5 reveals that, based on the test data, the residual analysis showed that for DOP, residuals were centered close to zero (mean\u0026thinsp;=\u0026thinsp;0.033, SD\u0026thinsp;=\u0026thinsp;0.434), indicating unbiased predictions but with moderate variability. WBW exhibited a similar near-zero bias (mean\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.009, SD\u0026thinsp;=\u0026thinsp;0.523), though the wider spread suggested less stability. In contrast, the D/W ratio displayed the most precise predictions, with residuals tightly clustered around zero (mean\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.002, SD\u0026thinsp;=\u0026thinsp;0.078). The absence of clear patterns across all plots confirms that the Ridge model maintained stability, even if certain responses involved higher variability.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure 6 presents the relationships among the predicted weld quality metrics. DOP and WBW showed a relatively strong correlation, as increases in welding current and certain fluxes tended to simultaneously enlarge both parameters. Consequently, fluctuations in one often influenced the other, and this coupling was reflected in the consistently high R\u0026sup2; values (\u0026gt;\u0026thinsp;0.83) across splits. In contrast, the D/W ratio behaved more independently, since it is a derived parameter that balances penetration against width. Its variation was strongly affected by small changes in both DOP and WBW, but neither variable alone could fully determine it, explaining that the D/W ratio resulted in lower validation accuracy (R\u0026sup2; = 0.667) despite maintaining very low prediction errors (RMSE\u0026thinsp;=\u0026thinsp;0.063\u0026ndash;0.093). Thus, while DOP and WBW were mutually reinforcing and strongly tied to process conditions, the D/W ratio introduced additional complexity, being less directly influenced by any single parameter and more sensitive to their combined fluctuations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs illustrated in Fig.\u0026nbsp;7, heatmaps of RMSE, MAE, and R\u0026sup2; highlight differences in predictive performance across the three targets. D/W ratio showed the lowest errors (RMSE\u0026thinsp;\u0026asymp;\u0026thinsp;0.07, MAE\u0026thinsp;\u0026asymp;\u0026thinsp;0.06), confirming its stability as a predictive variable. DOP had higher errors (RMSE\u0026thinsp;\u0026asymp;\u0026thinsp;0.38, MAE\u0026thinsp;\u0026asymp;\u0026thinsp;0.30) but the strongest correlation with parameters (R\u0026sup2; \u0026asymp; 0.87). WBW displayed the largest errors (RMSE up to 0.67, MAE up to 0.52) and weaker explanatory power (R\u0026sup2; \u0026asymp; 0.86), reflecting its dependence on complex effects such as arc stability and heat distribution. Overall, D/W ratio and DOP emerge as more robust and interpretable responses for TIG welding optimization, while WBW remains less predictable.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe Ridge regression model showed moderate predictive performance across the weld quality indicators (Fig.\u0026nbsp;8). For DOP, the model achieved R\u0026sup2; = 0.851, indicating accurate capture of welding current, Flux composition, and molten pool effects. WBW prediction performed best with R\u0026sup2; = 0.855, reflecting effective modeling of lateral heat distribution and arc constriction. The D/W Ratio exhibited the lowest absolute prediction errors (mean\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.002, SD\u0026thinsp;=\u0026thinsp;0.078) but a lower R\u0026sup2; = 0.743, owing to its compressed dynamic range, where small absolute deviations represent a larger proportion of total variance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003e3–3 XGBoost modeling:\u003c/h3\u003e\n\u003cp\u003eDue to the limited capability of Ridge regression, it was not sufficient for this study. Therefore, XGBoost was employed as the primary model, offering higher accuracy and robustness in predicting WBG. Hyperparameter tuning was carried out prior to presenting the XGBoost modeling results. As shown in Table\u0026nbsp;4, the Optuna-based search identified an optimal setup with n_estimators\u0026thinsp;=\u0026thinsp;194 and learning rate\u0026thinsp;=\u0026thinsp;0.160, providing fast yet stable convergence. A relatively high tree depth (max_depth\u0026thinsp;=\u0026thinsp;9) combined with min_child_weight\u0026thinsp;=\u0026thinsp;3 enabled the model to capture nonlinear dependencies while preventing overfitting. Regularization through sampling (subsample\u0026thinsp;=\u0026thinsp;0.657, colsample_bytree\u0026thinsp;=\u0026thinsp;0.633) further enhanced robustness by increasing model diversity. The tuning process was integrated with a K-fold cross-validation strategy, which ensured that the selected parameters generalized well across different subsets of the data.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eHyperparameters for XGBoost modeling\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003en_estimators\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003elearning_rate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003emax_depth\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003emin_child_weight\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003esubsample\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ecolsample_bytree\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e194\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.657\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.633\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe comparison of Ridge regression and XGBoost metrics is provided in Table\u0026nbsp;5. For DOP, XGBoost improved R\u0026sup2; from 0.869 to 0.956 with ~\u0026thinsp;43% error reduction; for WBW, R\u0026sup2; rose from 0.869 to 0.910 with ~\u0026thinsp;17% improvement; and for the D/W ratio, R\u0026sup2; increased from 0.771 to 0.870 with ~\u0026thinsp;25% lower RMSE. These results indicate that while Ridge regression can capture general trends, XGBoost more effectively models nonlinear interactions, delivering superior accuracy and robustness for weld geometry prediction.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparative performance of Ridge regression and XGBoost models for predicting weld geometry responses, including DOP, WBW, and D/W\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTarget\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR2 (test)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRMSE (test)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMAE (test)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDOP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.868997322\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.435989773\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.359490488\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRidge\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWidth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.86868184\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.524787275\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.46059194\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRidge\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD/W Ratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.770766489\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.078860262\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.068706048\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRidge\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDOP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.955894672\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.25297741\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.204567863\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eXGB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWidth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.910070433\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.434282324\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.340601983\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eXGB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD/W Ratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.870027603\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.05938062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.05101442\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eXGB\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;9, SHAP summaries for WBW and DOP identify welding current as the dominant factor. Higher currents increase heat input, enhancing penetration, widening the fusion zone, and raising the D/W ratio, while lower currents reduce these responses. Flux composition has a secondary influence: SiO₂ strongly enhances penetration and D/W ratio (D/W up to 0.79), TiO₂ provides balanced performance (D/W\u0026thinsp;~\u0026thinsp;0.6\u0026ndash;0.7), and ZnO/Al₂O₃ promotes bead widening (\u0026gt;\u0026thinsp;8 mm) but lower penetration.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4- Result and discussion","content":"\u003cp\u003eThis section provides a detailed analysis of the experimental results, focusing on the influence of flux compositional features on WBG. DOP and WBW are employed as the primary metrics for evaluating welding performance, as they jointly capture the balance between penetration capability and lateral heat distribution. DOP is a critical parameter because it reflects the extent of energy transfer into the workpiece and directly determines the load-bearing capacity and structural integrity of the weld. A high DOP indicates efficient utilization of arc energy and ensures sufficient fusion for single-pass welding in medium to thick sections [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. In contrast, WBW represents the degree of lateral spread of the molten pool, which strongly affects arc stability, heat distribution, and dimensional control. In TIG welding, a narrower WBW is generally preferred, as it reduces lateral heat dispersion and helps limit the heat-affected zone (HAZ). A smaller HAZ is beneficial since it minimizes undesirable microstructural transformations, grain coarsening, and the loss of mechanical properties such as hardness and toughness in regions adjacent to the weld [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAccording to the SHAP analysis (Fig.\u0026nbsp;9), SiO₂ was identified as the most influential flux on WBG. Experimental results showed that these fluxes increased WBW; however, penetration depth increased more significantly, leading to a marked improvement in the D/W ratio (e.g., from 0.499 to 0.793 for SiO₂) [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. This behavior reflects the arc constriction effect, which concentrates energy and drives deeper fusion into the base material. Although the bead became wider, the improved D/W ratio and the confinement of thermal influence into a deeper rather than wider profile effectively helped reduce excessive HAZ growth [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn order to rationalize the observed enhancement in DOP and the concurrent reduction in WBW under specific flux conditions, it is necessary to consider the fundamental transport forces acting within the weld pool. Among these, the Marangoni force, Lorentz (electromagnetic) force, buoyancy force, and aerodynamic drag force play decisive roles, and their relative magnitudes are strongly governed by the welding current, flux material composition, and arc behavior [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eA higher DOP generally indicates more efficient energy concentration at the weld root, while WBW reflects the lateral spread of heat and molten metal. Therefore, fluxes that simultaneously promote deeper penetration and restrict excessive bead widening are expected to yield higher D/W ratios. By examining the trends in DOP and WBW for each flux type, a mechanistic understanding can be developed regarding how arc constriction and Marangoni convection collectively govern the final D/W ratio [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFor the Marangoni force, the temperature-dependent surface tension gradient plays a central role in directing molten metal flow. Oxygen released from fluxes such as SiO₂ reverses the temperature coefficient of surface tension (dσ/dT\u0026thinsp;\u0026lt;\u0026thinsp;0), inducing inward-directed surface flow. This reverse Marangoni convection channels heat and molten metal toward the weld root, producing deeper penetration and limiting bead spreading [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. The strong D/W ratio achieved with SiO₂ at 160 A (0.794, +\u0026thinsp;46% compared to 0.545 at 80 A) is directly attributable to this mechanism. By contrast, fluxes with slower oxygen release, such as TiO₂ (0.653 at 160 A, +\u0026thinsp;100% improvement from 0.326 at 80 A) or those with low oxygen activity, like Al₂O₃ (0.347 at 160 A, only\u0026thinsp;+\u0026thinsp;14% compared to 0.304 at 80 A), generate weaker Marangoni reversal, resulting in shallower and wider bead profiles.\u003c/p\u003e \u003cp\u003eThe Lorentz force further reinforces penetration at elevated welding currents. As current increases, or when the arc is constricted by oxygen-rich fluxes, the local current density and self-induced magnetic field intensify. This electromagnetic body force drives molten metal downward and inward, enhancing DOP [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. As observed, SiO₂ showed a DOP increase from 1.58 mm at 80 A to 4.90mm at 160 A (+\u0026thinsp;210%), while TiO₂ improved even more dramatically from .30 mm to 4.25 mm (+\u0026thinsp;228%), confirming the dominance of Lorentz forces under high-current and oxygen-active flux conditionsAlthough both TiO₂ and SiO₂ are oxygen-rich oxides, SiO₂ proves more effective in supplying active oxygen to the weld pool because its superiority depends not only on stoichiometric oxygen content but also on its thermodynamic stability, decomposition kinetics, and oxygen chemical activity [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSiO₂ has a relatively lower Gibbs free energy of oxygen release in the arc temperature range, which promotes gradual and sustained liberation of oxygen ions. This controlled release stabilizes the arc plasma and ensures a steady reversal of Marangoni convection [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. In contrast, TiO₂ tends to release oxygen less efficiently due to its higher decomposition temperature and its strong affinity for oxygen, forming stable sub-oxides such as Ti₂O₃ that \u0026ldquo;trap\u0026rdquo; oxygen [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Consequently, despite similar nominal oxygen contents, SiO₂ delivers a higher effective oxygen activity to the weld pool, producing stronger arc constriction and more consistent inward molten flow [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. This clarifies why, under the same welding currents, SiO₂ consistently yielded the highest D/W ratio (0.794 at 160 A) compared to TiO₂ (0.653 at 160 A).\u003c/p\u003e \u003cp\u003eThe buoyancy force, arising from thermal expansion (\u0026prop; gβΔT), tends to spread heat laterally and widen the bead in conventional TIG welding. However, in the presence of strong reverse Marangoni and Lorentz forces, buoyancy acts more as a secondary stabilizing effect, reinforcing downward flow [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. This finding demonstrates that CaCO₃, despite its limited Marangoni activity, showed a substantial DOP increase from 0.87 mm at 80 A to 3.45 mm at 160 A (+\u0026thinsp;298%), yet the corresponding D/W ratio remained moderate (0.527 at 160 A).\u003c/p\u003e \u003cp\u003eFinally, the aerodynamic drag force, exerted by the plasma jet, plays a complementary role. When the arc is constricted, the plasma velocity and axial pressure increase, forcing molten metal toward the centerline. This aerodynamic drag complements Marangoni reversal and J\u0026times;B forcing, narrowing the bead and deepening penetration [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. However, in fluxes with unstable vaporization, such as ZnO, arc instability reduced this beneficial effect, leading to shallow penetration (1.08 \u0026rarr; 1.91 mm, +\u0026thinsp;77%) and wider beads (3.97 \u0026rarr; 8.57 mm, +\u0026thinsp;116%), which in turn decreased the D/W ratio from 0.270 at 80 A to just 0.223 at 160 A (\u0026minus;\u0026thinsp;18%). The welding. Across all fluxes, an increase in current from 80 A to 160 A substantially improved penetration; however, the net D/W ratio improvement depended on the balance between DOP gain and WBW widening [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFor SiO₂, the most effective flux, the DOP increased from 1.58 mm at 80 A to 4.90 mm at 160 A, corresponding to a 210% improvement. WBW expanded moderately from 3.55 mm to 6.17 mm (74% increase), yielding a final D/W ratio of 0.79 at 160 A compared to 0.545 at 80 A (46% enhancement). As summarized in Table\u0026nbsp;6, flux composition and welding current strongly affect weld geometry, with SiO₂ providing the highest D/W ratio (0.794 at 160 A) via stable Marangoni flow, while other fluxes show varying efficiency, highlighting the key role of oxygen-release kinetics.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of DOP, WBW, and D/W ratio across welding currents (80 \u0026rarr; 160 A) for different\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFlux\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDOP (mm) 80A \u0026rarr; 160A\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBead Width (mm) 80A \u0026rarr; 160A\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eD/W 80A \u0026rarr; 160A\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSiO₂\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.76 \u0026rarr; 4.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.51 \u0026rarr; 6.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.499 \u0026rarr; 0.793\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTiO₂\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.30 \u0026rarr; 4.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.97 \u0026rarr; 6.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.326 \u0026rarr; 0.653\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCaCO₃\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.87 \u0026rarr; 3.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.88 \u0026rarr; 6.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.223 \u0026rarr; 0.527\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCuO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.41 \u0026rarr; 3.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.87 \u0026rarr; 6.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.346 \u0026rarr; 0.593\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAl₂O₃\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.01 \u0026rarr; 2.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.30 \u0026rarr; 8.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.304 \u0026rarr; 0.338\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZnO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.08 \u0026rarr; 2.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.97 \u0026rarr; 8.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.270 \u0026rarr; 0.245\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\n\u003ch3\u003e4 − 1 Uncertainty Estimation Performance\u003c/h3\u003e\n\u003cp\u003eIn predictive modeling, UQ provides insight into the confidence of model outputs. Even when models achieve high accuracy, their predictions are not deterministic and carry associated uncertainty [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Two principal classes of uncertainty are typically distinguished. The first is aleatoric uncertainty, also referred to as data uncertainty, which arises from inherent variability or noise in the observed data. In welding and WAAM processes, aleatoric uncertainty is linked to uncontrollable micro-scale fluctuations such as melt pool turbulence, local arc instabilities, and measurement errors. Importantly, this type of uncertainty cannot be reduced simply by acquiring more data, as it reflects true randomness in the process. The second class is epistemic uncertainty, or model uncertainty, which results from incomplete knowledge of the underlying system or insufficient data to fully train the model. For instance, using a limited dataset or an inadequate model architecture introduces epistemic uncertainty. Unlike aleatoric uncertainty, epistemic uncertainty can be reduced through improved modeling strategies, additional data collection, or more expressive algorithms. Some frameworks additionally distinguish between optimistic and pessimistic uncertainty estimates, which reflect whether PIs underestimate or overestimate the true variability [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn the present work, uncertainty was quantified using quantile regression with XGBoost. Unlike conventional regression, which predicts the conditional mean, quantile regression estimates conditional quantiles of the response distribution, such as the 5th, 50th, and 95th percentiles. This allows direct estimation of PIs. For each target, models were trained to predict the lower bound (5th quantile), the median (50th quantile), and the upper bound (95th quantile). The interval between the 5th and 95th quantile provides a 90% PIs, which captures the variability in process outcomes [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. This approach directly addresses aleatoric uncertainty, since the width of the interval reflects inherent data variability.\u003c/p\u003e \u003cp\u003eThree XGBoost quantile models (0.05, 0.50, 0.95) were trained and optimized with pinball loss, yielding 90% PIs. On the independent test set (n\u0026thinsp;=\u0026thinsp;9), coverage was 66.7% for DOP, 77.8% for WBW, and 77.8% for D/W ratio, with normalized widths of ~\u0026thinsp;40\u0026ndash;44%. WBW performed best (R\u0026sup2; = 0.9242, RMSE\u0026thinsp;=\u0026thinsp;0.3774), DOP showed a strong fit (R\u0026sup2; = 0.8955) but poor coverage, and the D/W ratio had the lowest R\u0026sup2; (0.8080), though a reasonable interval width (39.95%). Interval width correlated with prediction error (r\u0026thinsp;=\u0026thinsp;0.5881), validating its role as an uncertainty indicator. The quantile regression framework extends beyond deterministic point predictions by explicitly establishing confidence bounds for model outputs. From a manufacturing perspective, this approach enables risk-informed decision-making, predictive quality assurance, and paves the way toward digital twin integration in Industry 4.0 welding environments [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eCoverage results (Table\u0026nbsp;7) show that the 90% PIs from quantile regression are under-dispersed for DOP (66.67% coverage) and better, but still short of nominal, for WBW and D/W Ratio (77.78% each). Although normalized interval widths are similar across targets (~\u0026thinsp;40\u0026ndash;44%), DOP's lower coverage indicates its predictive uncertainty is underestimated, likely owing to higher intrinsic variability or unmodeled nonlinear effects. Point-prediction metrics support this: WBW has the strongest performance (R\u0026sup2; = 0.9242, RMSE\u0026thinsp;=\u0026thinsp;0.3774) and the most reliable intervals; DOP shows a high R\u0026sup2; (0.8955) but moderate RMSE and poor coverage, implying extreme errors are underrepresented; D/W Ratio has the lowest R\u0026sup2; (0.8080) yet reasonably narrow intervals (39.95% normalized width), warranting cautious interpretation.\u003c/p\u003e \u003cp\u003eThe positive correlation between interval width and absolute prediction error (r\u0026thinsp;=\u0026thinsp;0.5881) confirms that wider intervals meaningfully reflect larger uncertainty, providing a valuable reliability indicator for model predictions. This correlation demonstrates that the quantile regression framework successfully captures the relationship between prediction uncertainty and error magnitude. Practically, WBW predictions are the most ready for industrial use, while DOP requires additional data or recalibration (or more conservative control margins); D/W Ratio predictions remain useful but should be treated with caution due to their compressed dynamic range. From a manufacturing perspective, this uncertainty-aware approach enables risk-informed decision-making and predictive quality assurance by identifying when predictions have higher uncertainty, paving the way toward more reliable welding process optimization in Industry 4.0 applications.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eUQ Performance Metrics of the XGBoost Median-Quantile Model on the Test Set.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTarget\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCoverage (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAvg Interval Width\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNormalized Width (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eR\u0026sup2;\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDOP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e55.55556\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.716195\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e44.47253\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.367877\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.906732\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWidth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e77.77778\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.390357\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e45.38365\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.440114\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.907639\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD/W Ratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e66.66667\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.219501\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e38.5766\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.068579\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.826643\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigures 10\u0026ndash;12 present the UQ analysis for DOP, WBW, and D/W Ratio, each evaluated with 90% PIs. For DOP (Fig.\u0026nbsp;10), only 55.6% of test samples fell within the PIs, revealing strong under-coverage compared to the nominal 90%. Interval widths ranged from 1.0 to 3.2, with a mean of 1.716, and four samples (0, 2, 6, 8) lay outside the bounds. While intermediate widths (1.5\u0026ndash;2.0) achieved full coverage, both very narrow and very wide intervals failed, indicating systematic underestimation of variability.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor WBW (Fig.\u0026nbsp;11), coverage improved to 77.8%, though still below the nominal level. Interval widths were relatively consistent, ranging from 1.75 to 2.75 with a mean of 2.390, producing sharp yet under-dispersed intervals. Calibration analysis revealed fluctuations, with some bins achieving full coverage and others none at all, emphasizing the need for recalibration despite the strong point-prediction accuracy (R\u0026sup2; = 0.9242).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor the D/W Ratio (Fig.\u0026nbsp;12), coverage again reached only 66.7%, with three of nine samples, particularly higher ratio cases, lying outside the intervals. Widths averaged 0.220, predominantly concentrated around 0.25\u0026ndash;0.27, where coverage reached 100%, while narrower intervals (~\u0026thinsp;0.18\u0026ndash;0.20) consistently failed. This imbalance highlights that the model tended to underestimate variability for smaller widths, resulting in inconsistent reliability.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAll three models retained strong predictive capability after integrating UQ. For D/W ratio, the model achieved an R\u0026sup2; of 0.8080 with an RMSE of 0.0677, confirming reliable point estimates alongside informative intervals. Normalized interval widths were consistent across targets (\u0026asymp;\u0026thinsp;40\u0026ndash;44%), indicating stable relative uncertainty irrespective of the output variable. However, coverage rates (55.6\u0026ndash;77.8%) revealed systematic under-coverage, with DOP performing worst (55.6%), followed by D/W ratio (66.7%) and WBW (77.8%). This underestimation stems from the stochastic multiphysics of TIG welding, transient fluid flow, heat transfer, and phase transformations, and the limited dataset size (n\u0026thinsp;=\u0026thinsp;36), which constrains generalization in extreme conditions. Despite these limitations, the stable interval widths suggest that the framework captured genuine process variability rather than output-specific artifacts. Furthermore, positive correlations between interval width and prediction error (0.20\u0026ndash;0.65) confirm that the intervals provide meaningful reliability information. In practice, narrow intervals can guide automated control and real-time parameter tuning, whereas wide intervals should trigger manual inspection or adaptive strategies, enabling risk-informed quality assurance.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study demonstrated the integration of systematic A-TIG welding experiments with ML and UQ for WBG prediction. Among the tested fluxes, SiO₂ produced the most favorable welds, achieving the highest D/W ratio of 0.794 at 160 A, while TiO₂ and CuO offered moderate improvements, and ZnO performed poorly. Ridge regression provided a stable linear baseline, but XGBoost more effectively captured nonlinear interactions, reducing predictive errors by approximately 20\u0026ndash;40%. UQ, through quantile regression, enabled the generation of 90% PIs, with empirical coverage ranging from 55.6\u0026ndash;77.8% across responses. The lowest coverage was observed for depth of penetration (55.6%), followed by D/W ratio (66.7%) and WBW (77.8%). Although the intervals underestimated variability, their normalized widths remained consistent at \u0026asymp;\u0026thinsp;40\u0026ndash;44% of the target domain, and they were positively correlated with prediction errors, confirming their value as indicators of predictive reliability.\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eProducing the highest D/W\u0026thinsp;=\u0026thinsp;0.794, SiO₂ had the highest DOP altered from 1.58 \u0026rarr; 4.90 mm (+\u0026thinsp;210%) and WBW from 3.55 \u0026rarr; 6.17 mm (+\u0026thinsp;74%).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eRaising current from 80 \u0026rarr; 160 A consistently increased penetration for all fluxes, but only SiO₂ and TiO₂ converted this into high D/W ratios because their oxygen release sustained inward flow; others mainly widened the bead.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eRidge regression explained 76\u0026ndash;87% of R\u0026sup2; with RMSE up to 0.66 mm, serving as a linear baseline. XGBoost outperformed it with R\u0026sup2; = 0.956 (DOP), 0.910 (WBW), 0.870 (D/W), and RMSE reduced to 0.25\u0026ndash;0.43 mm, i.e., 20\u0026ndash;40% lower errors, by capturing nonlinear effects of flux type and current.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eWelding current was the dominant factor; flux type came second. SiO₂ contributed the most to penetration and D/W, while ZnO widened the bead without penetration benefits.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eQuantile regression gave 90% PIs with coverage 55.6% (DOP), 77.8% (WBW), 66.7% (D/W), and normalized interval widths\u0026thinsp;\u0026asymp;\u0026thinsp;40\u0026ndash;44%. Under-coverage shows underestimation of variability, but the positive correlation (r\u0026thinsp;\u0026asymp;\u0026thinsp;0.59) between interval width and error proves the intervals are informative.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgment\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors sincerely thank the Faculty of Engineering at Ferdowsi University for their generous support in granting access to the necessary facilities and laboratories for this research. They also extend their deep appreciation to the anonymous reviewers for their thoughtful feedback and constructive suggestions, which have significantly contributed to improving the quality of this work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo funding was obtained for this study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of conflicting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors did not receive support from any organization for the submitted work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate and publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was conducted in accordance with the ethical guidelines outlined by the Committee on Publication Ethics (COPE). All participants provided written informed consent to participate in the study\u003cstrong\u003e.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of generative AI and AI-assisted technologies in the manuscript preparation process\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn the preparation of this manuscript, the authors utilized AI-assisted tools (DeepSeek and ChatGPT) to enhance writing clarity and coherence. Following AI assistance, the authors critically reviewed, revised, and validated the content, assuming full responsibility for all aspects of the published work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCRediT Author Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMahdi Mazloom Farsibaf\u003c/strong\u003e: Conceptualization, Methodology, Software, Investigation, Data Curation, Writing \u0026ndash; Original Draft, Writing \u0026ndash; Review \u0026amp; Editing, Visualization.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSeyed Moein Fareghi\u003c/strong\u003e: Investigation, Validation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eKiana Arteshyar:\u003c/strong\u003e Writing \u0026ndash; Original Draft, Writing \u0026ndash; Review \u0026amp; Editing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eKiarash Rahimi:\u003c/strong\u003e Methodology, Writing \u0026ndash; Original Draft.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDr. Farhad Kolahan:\u003c/strong\u003e Supervision, Project Administration, Resources, Writing \u0026ndash; Review \u0026amp; Editing.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eJiang Z et al (2024) Correlation analysis of current, molten pool, and weld formation in double-pulsed variable polarity TIG welding. 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Adv Neural Inf Process Syst 34:10971\u0026ndash;10984. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.48550/arXiv.2011.09588\u003c/span\u003e\u003cspan address=\"10.48550/arXiv.2011.09588\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"welding-in-the-world","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"witw","sideBox":"Learn more about [Welding in the World](https://www.springer.com/journal/40194)","snPcode":"40194","submissionUrl":"https://www.editorialmanager.com/witw/","title":"Welding in the World","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"A-TIG welding, Weld bead geometry, Modelling, Machine learning, XGBoost and Ridge regression, Uncertainty quantification","lastPublishedDoi":"10.21203/rs.3.rs-9530256/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9530256/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMachine learning (ML) modeling of Activated Tungsten Inert Gas (A-TIG) welding is challenged by the limited availability of experimental data. Within this research, uncertainty quantification of ML-based predictions of weld bead geometry (WBG) was investigated for AISI 304L stainless steel (SS304L) welded with six micro-sized activating fluxes (SiO₂, TiO₂, Al₂O₃, ZnO, CuO, CaCO₃). A design Matrix consisting of 45 runs was conducted, and depth of penetration (DOP), weld bead width (WBW), and the DOP-to-WBW (D/W) ratio were selected as evaluation parameters of WBG. Two predictive approaches were considered: Ridge regression as a linear baseline and Extreme Gradient Boosting (XGBoost) to capture nonlinear effects. Ridge regression provided moderate predictive performance, whereas XGBoost demonstrated superior accuracy with a determination coefficient (R\u003csup\u003e2\u003c/sup\u003e) of 96%. Experimental results confirmed SiO₂ as the most effective flux, achieving a depth-to-width ratio (D/W) of approximately 0.794 at 160 A, consistent with the mechanism of flux-induced arc constriction and Marangoni reversal that enhances DOP. Uncertainty quantification (UQ) was performed using quantile regression. 90% prediction intervals (PIs) achieved empirical coverages between 56% and 78% across targets (worst for DOP). The correlation between interval width and prediction error indicated that the UQ framework provided informative, though under-confident, estimates of predictive reliability. These results establish a combined experimental\u0026ndash;computational approach for uncertainty-aware modeling of A-TIG weld geometries, supporting more reliable process design and advancing the integration of ML in welding modeling.\u003c/p\u003e","manuscriptTitle":"Machine Learning and Uncertainty Quantification for Predicting Weld Bead Geometry of AISI 304L in Micro-Size A-TIG Welding","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-16 14:56:44","doi":"10.21203/rs.3.rs-9530256/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2026-05-11T07:43:48+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-06T13:24:22+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Welding in the World","date":"2026-05-01T10:47:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-28T06:01:38+00:00","index":"","fulltext":""},{"type":"submitted","content":"Welding in the World","date":"2026-04-26T04:03:10+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"welding-in-the-world","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"witw","sideBox":"Learn more about [Welding in the World](https://www.springer.com/journal/40194)","snPcode":"40194","submissionUrl":"https://www.editorialmanager.com/witw/","title":"Welding in the World","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"58774444-1f7e-436b-90cb-1fa4a5b2272b","owner":[],"postedDate":"May 16th, 2026","published":true,"recentEditorialEvents":[{"type":"reviewerAgreed","content":"","date":"2026-05-11T07:43:48+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-06T13:24:22+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Welding in the World","date":"2026-05-01T10:47:06+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-16T14:56:45+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-16 14:56:44","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9530256","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9530256","identity":"rs-9530256","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}