The base material selected for this investigation was AISI 1020 mild steel, cut into coupons measuring 100 mm × 50 mm × 6 mm. ER70S-6 filler wire was used for all welds. Chemical uniformity was confirmed through supplier certification. Prior to welding, samples were cleaned with acetone to remove surface contaminants, ensuring reliable arc initiation.

Figure 1. Miller Synchrowave 350 LX TIG welding machine/Butt Welded Joint.

Welding was performed using a Miller Synchrowave 350 LX TIG machine (Figure 1) configured with Direct Current Electrode Negative (DCEN) polarity. A 2.4 mm diameter 2% thoriated tungsten electrode was employed, with 99.99% pure argon serving as the shielding gas. A square groove butt joint with a 2 mm root gap was utilized to simulate industrial practices. The welding was conducted in a single pass without edge beveling, as the 6 mm thickness allowed for adequate penetration. The torch was maintained at a travel angle of 70˚ to 80˚ relative to the workpiece, and the plates were rigidly clamped to a steel backing fixture to minimize excessive movement while accommodating thermal expansion.

Four critical process parameters were identified: Current (A), Voltage (V), Travel Speed (S), and Gas Flow Rate (GFR). The experimental design was structured using Response Surface Methodology (RSM) based on a Face-Centered Central Composite Design (FCCD). The parameters were varied across five levels, coded from −1 to +1 for the factorial points, with the axial points located at α = 1 (face-centered). The design comprised 16 factorial points, 8 axial points, and 6 center-point replicates (coded as 0), resulting in a total of 30 experimental runs (Table 1).

Table 1.Welding parameters and levels.

Post-weld, samples were sectioned at the mid-length transverse cross-section. The cross-sections were mounted, ground, polished, and etched using a 2% nital solution to reveal the macrostructure. The Fusion Zone (FZ) width was measured metallographically using an optical microscope equipped with digital image analysis software. To ensure accuracy, three readings were taken across the width of the fusion zone at the mid-thickness and averaged for each plate. All measurements were conducted after the samples had completely cooled to room temperature to eliminate thermal expansion effects. The dataset was cleaned and normalized prior to modeling. For ANN development, the data was randomly partitioned into training (70%), validation (15%), and testing (15%) subsets to ensure unbiased evaluation of generalization capability.

Response Surface Methodology (RSM): A second-order polynomial model was fitted using Design-Expert Version 13. The model adequacy was verified using Analysis of Variance (ANOVA), lack-of-fit tests, and diagnostic plots.

Artificial Neural Network (ANN): Modeling was performed using MATLAB 2021a Neural Network Toolbox. A feedforward backpropagation network with a 4-10-1 architecture (4 inputs, 10 hidden neurons, 1 output) was selected. The number of hidden neurons was determined empirically through a trial-and-error tuning process, testing hidden layers ranging from 4 to 15 neurons. The 10-neuron configuration was chosen as it minimized the Mean Squared Error (MSE) on the validation set without causing overfitting, aligning with the heuristic range suggested by standard neural network design principles. To establish a baseline and highlight the advantage of the nonlinear mapping capability of the ANN, a simple Multiple Linear Regression (MLR) model was also developed. The MLR model yielded a significantly lower R² of 0.76, confirming that the ANN architecture provides a substantial improvement in capturing the complex, nonlinear interactions of the welding process. The network was trained using the Levenberg-Marquardt algorithm. The Tangent Sigmoid function was used for the hidden layer, and a linear function for the output layer.

Presented in Table 2 is the experimental results for Fusion Zone width. Review of the experimental dataset indicates that the maximum Fusion Zone width of 11.23 mm was achieved in Run 21, corresponding to a Current of 150 A, Voltage of 20 V, Travel Speed of 50 mm/s, and Gas Flow Rate of 13 L/min. This condition represents the optimal balance of heat input and fluid dynamics within the tested domain. RSM and ANN predictions are compared to these experimental results.

Table 2. Experimental result.

The fit summary indicated that the quadratic model was statistically superior to linear and two-factor interaction models. The quadratic model yielded a sequential p-value of 0.0002 and a non-significant lack-of-fit (p = 0.2681), confirming adequacy (See Table 3).

Table 3. Fit summary for fusion zone width.

Model significance and Lack of Fit are presented in the ANOVA shown in Table 4. The model was significant and Lack of Fit was not significant, which agrees with literature for quadratic modeling.

The model exhibited a high coefficient of determination (R² = 0.9765) and adjusted R² = 0.9545 as presented in Table 5. The adequate precision ratio of 27.7872 indicated an excellent signal-to-noise ratio. All main effects (Current, Voltage, Speed, GFR) were significant (p < 0.05). Notably, Gas Flow Rate showed the highest F-value (96.82), suggesting a dominant influence on FZ width within the tested range. Interaction terms such as Current × Speed (AC) and Voltage × GFR (BD) were also significant, highlighting the complex interplay of parameters.

Table 4. ANOVA for quadratic model (FZ width).

Table 5. Fit statistics for FZ width.

The final predictive model is expressed in Equation (1)

Diagnostic plots (Predicted vs. Actual) showed data points closely aligned along the 45˚ line, confirming model reliability. However, Run 28 was identified as a potential outlier with a high studentized residual (3.317), warranting caution in extreme parameter regimes. The middle contour plot and the right 3D surface plot visualize the relationship between two input parameters, Current (Amp) and Voltage (Volt), and the resulting response variable, Fusion Zone (mm). Together, these visualizations help engineers understand how varying welding settings influences the weld geometry, allowing them to identify optimal parameter combinations to achieve a specific fusion zone size (Figure 2Figure 2).

Figure 2. Predicted vs actual/contour and surface Plot.

The ANN architecture (4-10-1) was trained until the validation error showed no improvement for six consecutive epochs, stopping at epoch 08 to prevent overfitting. The neural network model was trained using the Levenberg-Marquardt backpropagation algorithm with a random data division strategy to optimize performance based on Mean Squared Error (MSE). As illustrated in the central performance plot, the training process was monitored over eight epochs, with the best validation performance of 0.94191 achieved at epoch 2, indicated by the green circle. Following this epoch, the validation error began to increase while the training error continued to decrease, signaling the onset of overfitting and justifying the selection of epoch 2 as the optimal stopping point. The predictive capability of the model is further substantiated by the regression analysis presented in the right panel, which compares the network output against target values. The correlation coefficients (R) for the training, validation, and test sets were calculated to be 0.8894, 0.8741, and 0.9215, respectively, with an overall R value of 0.8892 for the entire dataset. These results indicate a strong linear relationship between the predicted and actual values, confirming the robustness and generalization ability of the developed neural network (Figure 3Figure 3).

Figure 3. Training interface settings/performance plot/regression plots.

A direct comparison of predictive capabilities presented in Table 6 revealed distinct strengths for each model.

Table 6. Comparison between RSM and ANN predictions.

Statistical Fit: RSM provided a higher coefficient of determination (R² = 0.9765) compared to ANN (R² = 0.889) within the experimental design space. This suggests RSM is highly effective for interpolation within the defined CCD limits as observed in Figure 4Figure 4 and Figure 5Figure 5.

Figure 4.Fitted line plot for Fusion Zone (RSM).

Figure 5.Fitted line plot for FZ Width (ANN).

Nonlinearity and Edge Cases: Time series plots (Figure 6Figure 6) indicated that ANN predictions tracked experimental values closely in runs involving extreme parameter combinations (e.g., Runs 25 - 30), where RSM showed slight deviations. This aligns with the theoretical advantage of ANN in capturing complex, higher-order nonlinearities that quadratic polynomials may miss.

Figure 6.Comparison time series plot.

Figure 4Figure 4 (Fitted Line Plot) comparisons confirmed that while RSM offers a tighter fit (S = 0.237) for the training data, ANN provides a robust alternative for scenarios where explicit mathematical relationships are difficult to define.