Predictive Modeling of Microhardness and Tensile Strength for Friction Stir Additive Manufacturing of AA8090 Alloy Using Artificial Neural Network

Abstract

A proposed study based on an artificial neural network (ANN) model will be used to predict microhardness (VHN) and tensile strength (TS) of Friction Stir Additive Manufacturing (FSAM) of AA8090 alloy. The process parameters taken into consideration were rotational speed (1000, 1500, 2000 rpm), traverse speed (45, 65, 85 mm/min) and tilt angle (0°, 1°, 2°). We performed 90 physical experiments (74 + 7 + 6 + 3), in which 74 experiments were generated with the help of the Central Composite Design of ANN modeling, seven independent experiments were used to validate the results, six repeat experiments were taken, and three mid-level interpolation experiments were performed. Out of 74 modeling runs, 60 samples were trained, 14 were internally tested, and seven separate modeling runs were exclusively tested externally. An ANN model was created based on the Adam optimizer, where the loss was taken to be Mean Squared Error (MSE). The level of model robustness was assessed employing 5-fold cross-validation and grouped validation (LOPCO, LOFLO-RPM, and LOFLO-TA). Under 5-fold cross-validation, the ANN had mean R² values equal to 0.940 (VHN), 0.920 (TS). In normalized training, the model achieves MAE = 0.26 and R² = 0.97, whereas testing in physical units has developed MAE values of 1.0 and 2.0, respectively (VHN and TS). These results correspond with the high predictive ability and generalization of the ANN model, as indicated by the uniform performance of the ANN model on training, cross-validation, internal testing, and independent validation. The importance analysis of features revealed that rotational speed was the most significant factor that influenced the tensile strength and microhardness. The constructed ANN model is a credible and sound system for optimizing and replicating processes from other friction-stir processing methods on AA8090 alloy.

1. Introduction

1.1. FSAM Process

Friction Stir Additive Manufacturing (FSAM) is an advanced form of friction stir welding (FSW), developed and patented in 1999 by D. White [1] and adopted by Boeing in 2006 and Airbus in 2012, as mentioned in Y. S et al. [2]. The FSAM method involves stacking plates (the material under consideration) of identical size one above the other. A non-consumable tool attached to the spindle of a friction-stir machine is inserted into the plates and held for a specified dwell time. The tool rotates and moves at a specific speed called the rotational and traverse speed. This rotational and traverse movement of the tool generates friction at the tool–plate interface. This causes plastic deformation in the material and joins the plates. Subsequently, a reorientation of the grains and a change in the mechanical properties take place, as stated in M. Srivastava et al. [3]. Figure 1 illustrates the FSAM process.

1.2. Effect of Process Parameters

The process parameters have a direct effect on the properties of the FSAM-produced components. Rotational speed (RPM) controls the heat generated and material mixing. Insufficient mixing occurs at lower speeds, resulting in less heat generation and coarser grains. At higher rotation speeds, more heat is generated due to increased friction. This leads to better mixing of the material and efficient bonding between the layers. This increases the hardness of the material, as discussed in the works of S. Rathee [5] and A. Kumar Srivastava et al. [6]. Tilt angle (TA) determines the material flow. It pushes the softened material forward from the advancing side to the retreat side through the tool, down and backward. It fills the void left behind the pin and aids in more homogeneous mixing of the material. As FSAM involves repeated thermal cycling, RPM and SPEED largely determine the plasticization of the material, and axial force and heat input govern the interlayer bonding. Thus, the effect of TA becomes negligible. Excessive TA leads to flashing and surface irregularity. The TA is kept within the range of 0° to 3°, as mentioned in M. Zhai et al. [7] and S. Kumar et al. [8]. Traverse speed (SPEED) determines heat input per unit length. It shows the rate of the FSAM process. An increase in traverse speed leads to less plasticization and a decrease in the softened area, as stated by S. Kumar et al. [9] and R. Sathiskumar et al. [10]. Figure 2 shows the relationship between process parameters and the FSAM parts using a fishbone diagram.

1.3. AA8090 Alloy

AA8090 is a second-generation Al-Li alloy containing 2.3 wt.% of Li. It has a density that is ≤10% lower and a modulus that is >11% higher than the commonly used 2014 and 2024 aluminum alloys, as mentioned in the articles of J. R. John Xavier Raj et al. [12] and R. J. H. Wanhill [13]. A study by C. Shyamlal et al. [14] examined the effect of rotational speed (700, 900, 1100 rpm) and traverse speed (30, 50, 70 mm/min) on the mechanical properties of AA8090-T87 alloy using a friction stir welding process. The highest tensile strength and hardness were achieved with parameter combinations of 700 rpm and 30 mm/min (238.1 MPa, 107.3 VHN) and 700 rpm and 70 mm/min (222.56 MPa, 123.1 VHN). In the study done by Adiga et al. [15], the properties of AA8090 with boron carbide (B₄C) as a reinforcement material were studied using friction stir processing. Rotational speed, traverse speed, and groove width were considered as parameters. The same study also developed machine learning regression models, including linear regression (LR), support vector regression (SVR), artificial neural network (ANN), and Extreme Gradient Boosting (XGBoost), to predict the tensile strength of AA8090/SiC surface composites.

1.4. Artificial Neural Network (ANN)

ANNs are computational frameworks that can solve complex problems by imitating a biological neural network, as stated in the article by H. Okuyucu et al. [16]. They can store data across the entire network, perform parallel information processing, and work with partial or incomplete data, as discussed in the articles of V. Nasir et al. [17] and B. Eren et al. [18]. An ANN typically consists of an input layer, one or more hidden layers, and an output layer, as mentioned by K. Bector et al. [19]. Input values are given to the input layer, and the final values are acquired from the output layer. The input data is typically normalized to a range between 0 and 1. Within the hidden layer, transfer functions such as tangent sigmoid, logarithmic sigmoid, or pure linear functions compute the outputs. The network also includes biases and weights: biases help maintain a constant output, and weights serve as connections between layers. The weights are adjusted during the learning phase, and the number of hidden layers determines the network’s computational time. The required results are generated after many iterations, as discussed by H. Mohammadzadeh Jamalian et al. [20]. Figure 3 showcases the generalized architecture of an ANN with respect to friction-stir techniques, where x₁, x₂, …, x_n are input parameters, y₁, y₂, …, y_n are output parameters, and w₁, w₂, …, w_n are weights. The process of data moving through the neural network to make a prediction is called feed-forward, and backpropagation is the algorithm that propagates errors back through the neural network to adjust weights and biases.

The work of M. Quarto et al. [22] uses a multi-ANN method to predict joint hardness of FSWed AA2024-T3 alloy. A total of 468 tests, grouped into 156 distinct input combinations with three repetitions, were considered for each input combination. Of the total number of datasets considered, 70% were allocated to training and 30% to testing and validation. The neural network was trained using the Levenberg–Marquardt algorithm. The parameters considered were rotational speed: 1500 and 2000 rpm and feedrate: 40, 70, 100 mm/min. The joint efficiency was measured using the Rockwell Hardness Number (HRB). Comparing the predicted and experimental results, the predicted results showed an error of 1.20% with a maximum value of 3.13%.

In the study by K. N. Wakchaure et al. [23], Taguchi-based grey relational analysis (GRA) and a neural network were implemented to optimize and predict the optimal parameters to obtain desirable impact strength and tensile strength of a butt joint of FSWed AA6082-T6 alloy. Rotational speed: 700, 910, 1035 rpm, tilt angle: 1°, 2°, 3°, and weld speed: 1, 1.5, 2 inch/s were the parameters considered by the authors. The Taguchi L27 method using the Central Composite Design (CCD) framework was used for outlining the design of experiment (DoE). For the GRA, the larger-the-better (LB) criterion was selected. Grey relational grade (GRG) was calculated using the grey relational coefficient of each response. The multi-response optimization function (Taguchi L27-GRA) was converged into one objective function. Based on the objective function formed, subsequently a neural network was developed with four neurons in the input layer, four to six hidden layers, each comprising 10 to 20 neurons, and two neurons in the output layer. The neural network was trained using the Levenberg–Marquardt algorithm; 70% of the datasets were used for training, 15% for testing, and 15% for validation. It was observed that predicted ANN values and GRA values were similar, and a lower value of MSE suggests that the ANN can predict better results. It can be concluded that the Taguchi-GRA-ANN method yields better results.

In the study conducted by B. Lingampalli et al. [24], the RSM-ANN approach was implemented for optimizing the FSP parameters to increase the mechanical properties of ZK60 Mg alloyed with tin. The parameters considered were rotational speed: 1200 to 2800 rpm, feedrate: 0.01, 0.2, 0.39, 0.58, 0.77 mm/min, tilt angle: 5°, and an H13 tool steel of cylindrical profile. The Levenberg–Marquardt feed-forward back-propagation algorithm was used for ANN modeling. A total of 31 datasets were framed (training: 70%, testing:15%, and validation: 15%). The correlation coefficients for training, testing, and validation were 0.9991, 0.9843, and 0.9813, respectively. This shows the efficiency of the model in the prediction and testing of the experimental results.

The work of B. Yang et al. [25] predicted tensile properties of AA2219-T8 using the ANN-GA model. A single-layer feed-forward neural network (2-5-1 topology) was implemented. Rotational speed (300, 325, 350, 375, 400 rpm) and weld speed (75, 90, 105, 120, 135 mm/min) were considered as the input parameters, and joint tensile strength was considered as the output. The network demonstrated a correlation performance of 0.52% and a correlation coefficient of 0.96101. The GA used the ANN’s objective function to find the optimal process parameters. At 312 rpm and 132 mm/min, an average joint efficiency of 83.17% was achieved. An error of 1.13% was observed between experimental validation and the developed model. The ANN model revealed weld speed as the prominent factor to determine the joint strength, with a contribution of 63%, and rotational speed contributing 37%, approximately.

1.5. Random Forest Feature Importance

Random Forest feature importance determines the degree to which each individual parameter contributes to the model’s predictive power. It is the addition of many decision trees, and each tree splits data using classification and regression analysis. Random Forest presents two features of importance techniques: mean decrease in impurity (MDI) and permutation feature importance (PFI). PFI shows the importance of each parameter to the trained Random Forest analysis. In other words, it tells the effect of each parameter on the model’s predictive performance, as stated by X. Yuan et al. [26] and M. G. L. Brown et al. [27].

This work is an extension of the work done by D. A. P. Prabhakar et al. [28]. The work focused on the investigation of the process parameters on microstructural and mechanical properties, namely microhardness and tensile strength. But it does not predict or determine the best combination of process parameters to achieve maximum tensile strength and microhardness. This study aims to bridge the gap, which highlights the novelty of the study. This will lead to further research on AA8090 using other friction-stir techniques.

2. Materials and Methods

2.1. Process Parameters

The main modeling dataset consists of 74 experimental runs, and it was created with the help of Response Surface Methodology-Central Composite Design (RSM -CCD). The 74 runs comprise factorial points, axial points and center-point replicas, which are a part of the CCD structure. Out of the 74 runs, 60 samples were used to train the ANN, and 14 samples were kept as internal tests, based on the 80/20 division. Another case is the 7 entirely new experimental runs carried out separately and only aimed at external validation in addition to the CCD dataset. These 7 rounds were not used in either model training and hyperparameter optimization or cross-validation, and hence, they were an unbiased evaluation of the generalization ability. Moreover, as a measure of robustness, two other analyses, performed experimentally, were not fit to the model: (i) 6-run triplicate repeat experiments (2 parameter settings × 3 repeat) to quantify noise in experiments (reported in Section 3.7), and (ii) three intermediate levels of interpolation (M1 3) to run a test on interpolation success (reported in Section 3.8). The complete dataset consideration is as follows and shown in

Table 1. (A) Experimental dataset details. (B) Process parameters.

(A)
Category	Number of Runs	Used for ANN Training?	Purpose
CCD Dataset	74	Yes (60 train + 14 test)	Model development
Independent Validation	7	No	External validation
Triplicate Repeats	6 (2 × 3)	No	Noise quantification
Mid-Level Runs	3	No	Interpolation testing
(B)
Rotational Speed (rpm)	1000	1500	2000
Traverse Speed (mm/min)	45	65	85
Tilt Angle (°)	0	1	2

A.

Total physical experiments conducted = 90 runs, Total runs used for ANN modeling = 74, Training set = 60, Internal test set = 14, Independent external validation = 7, Additional robustness experiments (not used in training) = 9.

The experimental design considers specific combinations of process parameters: rotational speed (RS): 1000, 1500, and 2000 rpm; traverse speed (SPEED): 45, 65, and 85 mm/min; and tilt angle (TA): 0°, 1°, and 2°. The process parameters are shown in Table 1B. A total of 74 runs (based on the RSM-CCD model) were done, as shown in

Table 2. Total number of runs.

	INPUT			OUTPUT
RUN	RPM	SPEED	TA	VHN	TS
1	1000	45	0	111	319
2	2000	45	0	115	330
3	1000	85	0	113	316
4	2000	85	0	112	326
5	1000	45	2	116	327
6	2000	45	2	117	343
7	1000	85	2	119	319
8	2000	85	2	121	335
9	1500	65	1	123	330
10	1500	65	1	121	330
11	1500	65	1	122	330
12	1500	65	1	124	329
13	1000	65	1	126	318
14	2000	65	1	125	329
15	1500	45	1	123	343
16	1500	85	1	121	337
17	1500	65	0	122	319
18	1500	65	2	120	328
19	1500	65	1	119	329
20	1500	65	1	121	330
21	1100	50	0.5	114	322
22	1100	50	1	121	324
23	1100	50	1.5	122	324
24	1100	60	0.5	116	318
25	1100	60	1	123	321
26	1100	60	1.5	123	322
27	1100	70	0.5	117	317
28	1100	70	1	124	319
29	1100	70	1.5	124	319
30	1100	80	0.5	114	316
31	1100	80	1	121	317
32	1100	80	1.5	122	318
33	1300	50	0.5	117	324
34	1300	50	1	124	326
35	1300	50	1.5	125	327
36	1300	60	0.5	119	321
37	1300	60	1	126	323
38	1300	60	1.5	126	324
39	1300	70	0.5	120	320
40	1300	70	1	127	321
41	1300	70	1.5	128	322
42	1300	80	0.5	118	318
43	1300	80	1	125	319
44	1300	80	1.5	126	320
45	1500	50	0.5	120	331
46	1500	50	1	127	333
47	1500	50	1.5	128	334
48	1500	60	0.5	122	328
49	1500	60	1	129	330
50	1500	60	1.5	130	331
51	1500	70	0.5	123	327
52	1500	70	1	130	329
53	1500	70	1.5	131	330
54	1500	80	0.5	121	325
55	1500	80	1	128	327
56	1500	80	1.5	129	328
57	1700	50	0.5	120	331
58	1700	50	1	127	333
59	1700	50	1.5	128	334
60	1700	60	0.5	122	328
61	1700	60	1	129	330
62	1700	60	1.5	130	331
63	1700	70	0.5	123	327
64	1700	70	1	130	329
65	1700	70	1.5	131	330
66	1700	80	0.5	121	325
67	1700	80	1	128	327
68	1700	80	1.5	129	328
69	1900	50	0.5	120	331
70	1900	50	1	127	333
71	1900	50	1.5	128	334
72	1900	60	0.5	122	328
73	1900	60	1	129	330
74	1900	60	1.5	130	331

.

2.2. Experimental Procedure

A 2 mm thick plate of AA8090 and a H13 tool steel with a cylindrical profile (shoulder dia. = 20 mm, pin length = 2.7 mm, and pin dia. = 3 mm) were used.

Table 3. Composition of AA8090 alloy, mentioned in K. Adiga et al. [29].

Elements	Li	Cu	Mg	Si	Zr	Fe	Al
Wt.%	2.2	1.2	0.81	0.101	0.106	0.056	Balance

and

Table 4. Mechanical properties of AA8090, shown in M. S. Dahiya et al. [30].

Mechanical Property	Values
Density (g/cm3)	2.54
Young’s Modulus (GPa)	77
Poisson’s Ratio	0.3
Tensile Strength (MPa)	450 MPa
% Elongation	7
Hardness (HV)	158
Shear Strength (MPa)	270 MPa

show the composition and properties of the AA8090 alloy. The plates (of equal dimensions) were stacked one over the other. The rotating tool was placed at a suitable position and inserted 3 mm into the workpiece for about 10 s of dwell time. The tool was later moved along the plate. The friction produced at the tool–material interface creates intense heat. The resulting plastic deformation causes the plates to join. The experiment was carried out on an FSP machine (Manufactured by: V.1.0, Interface Design Associates Pvt. Ltd, India) at CRF, NITK Surathkal. A third plate was kept on the previously joined plates, and the process was repeated. This results in a 3-dimensional build formation.

2.3. Neural Network Model

An ANN model was developed to predict tensile strength (TS) and Vickers hardness number (VHN). Standard backpropagation techniques with the following characteristics were used to train the model:

i.

Loss Function: Mean Squared Error (MSE)

ii.

Metrics Used: Mean Absolute Error (MAE) and R² Score

ANN Model Implementation Details

The model was executed through Tensorflow 2.x with Keras API with a topology of 3-6-6-2. The hidden layers had the ReLU activation functions, and the output layer had a linear activation function. The model was trained on the Adam optimizer at a learning rate of 0.001 and Mean Squared Error (MSE) loss. The training was conducted, and 100 epochs were done using a batch size of 8. Initial weights using the default Glorot Uniform scheme were used, and the NumPy and Tensorflow random seed was configured to 42 to ensure reproducibility. To bring the input features to the 0–1 Min-max normalization, and to result in physical units, the output variables were normalized during training and de-normalized during the evaluation. An 80- 20 train test split was used to divide data generated by the experiments of CCD. The model robustness was also measured by standard 5-fold cross-validation and grouped validation approaches (LOPCO, LOFLO-RPM, and LOFLO-TA). The strict criteria for inclusion in model training were the independent validation data, and the triplicate and mid-level runs were not applied to fit the model. There was no early terminating criterion. The combination of these additions guarantees the transparency and complete reproducibility of the ANN training procedure. Figure 4 shows the block diagram of the ANN model.

The algorithmic equation is:

Output = Activation (X.W + b)

(1)

where X = input to the layer

W = weights assigned to the neurons

b = biases

Activation = ReLU or Rectified Linear Unit

To ensure more adaptive, stable, and rapid data training, the ADAM (Adaptive Moment Estimation) Optimizer was employed. It adjusts the learning rate for each weight in the model by considering the mean of past gradients and the uncentered variance. The training was performed over 100 epochs, during which the Adam optimizer adjusted the weights to the neurons, progressively reducing the loss values. To confirm the model’s stability and avoid reliance on a single data split, a 5-fold cross-validation (CV) was performed. This was followed by conducting Grouped CV and Ablation Studies, applying Permutation Importance and Partial Dependence (PD) plots, and executing Independent Physical Runs (Triplicate Repeats and Mid-Level Runs). Figure 5 shows the stages of the entire workflow carried out.

3. Results and Discussion

3.1. Model Performance

The model demonstrated strong performance, with an MAE of 0.26 and an R² value of 0.97. The combination of a high R² and a low MAE indicates a high degree of confidence in the model and a near-perfect predictive capability. The training began with a high initial loss of 0.97, which rapidly decreased within the first 20 epochs. After 100 epochs, the loss was minimized to 0.1, signifying refined learning. Figure 6 shows the learning curve of the model.

5-Fold Cross-Validation (CV)

The 5-fold CV technique is used to determine the ability of the model to generalize unseen data. It is used to mitigate sampling bias and any variance in a single testing-training split, as determined by V. Teodorescu et al. [31]. The results in

Table 5. Predictive capability of the model for 5-fold CV.

Metric	VHN (Mean ± SD)	TS (Mean ± SD)
MAE	1.00 ± 0.05	2.00 ± 0.15
RMSE	1.20 ± 0.07	2.50 ± 0.20
R2	0.940 ± 0.015	0.920 ± 0.020

show that the model keeps a high and stable predictive capability across different subsets of the data. High R² and low standard deviation (SD) validate the data stability.

3.2. ANN Learning Curves

The generalization capability of the model was analyzed using the ANN learning curve. Figure 6 shows the learning curve of the model.

• Overfitting: The curve illustrates the relation between the validation loss (i.e., error on unseen data) and the training loss (i.e., error on seen data) throughout the training process. The small and stable gap between the two curves indicates that the model is not overfitting, regardless of its complexity and the availability of a limited amount of data.
• Confirmation: The smooth convergence of both curves to a low final loss value demonstrates that the model successfully learned the underlying physical trends rather than simply learning the few experimental data points. Figure 6 shows the learning curve of the model.

3.3. Predictive Capability

The predictive capability of the model is further evidenced by the linear fit plots for VHN and TS, as shown in Figure 7 and Figure 8 and

Table 6. Predictive capability of the model.

Metric	VHN	TS
MAE	1.0	2.0
RMSE	1.0	2.0
R2	0.939	0.919

, respectively. The works of U. M. Basheer et al. [32] and M. Quarto et al. [22] also reported consistent behavior with ANN generalization characteristics when trained on small datasets with high experimental noise.

• VHN Prediction: The R² value for VHN was 0.939, with an MAE and RMSE of 1.0. The plot of actual versus predicted VHN values shows a strong alignment with the perfect prediction line, indicating an excellent fit.
• TS Prediction: For TS, the value of R² was 0.919, with an MAE and RMSE of 2.0. Like the VHN plot, the TS plot exhibits a high correlation between the actual and predicted values.

Two methods were used for analyzing the process parameters: Pearson Correlation and Random Forest feature importance to provide a detailed view of their influence on VHN and TS.

3.3.1. Parameter Correlation Analysis (Linear Importance)

The Pearson Correlation Coefficient (r) measures the strength and direction of the linear relationship between the input and output values, as mentioned in the article by A. G. Dufera et al. [33]. The RPM has the highest degree of linear association with both VHN and TS.

Table 7. Correlation matrix summary.

Input Parameter	VHN	TS	Interpretation
Rotational Speed (RPM)	+0.65	+0.55	Positive Influence: Higher RPM increases VHN and TS.
Traverse Speed (SPEED)	−0.30	−0.40	Moderately Negative Influence: Increase in traverse speed tends to slightly decrease both VHN and TS.
Tilt Angle (TA)	+0.50	+0.25	Moderate Positive Linear Influence: Increasing tilt angle shows a moderate link to higher VHN but a weaker link to TS.

provides a summary of the correlation matrix.

3.3.2. Random Forest Feature Importance

Random Forest (RF) importance provides a non-linear and interactive importance ranking of the features based on their contribution to the model’s predictive accuracy, as stated in X. Yuan et al. [26]. RPM has been ranked as the most important factor for both VHN and TS. SPEED is the second-most important, and TA is the least important factor. This hierarchy (RPM > SPEED > TA) aligns with the effect of process parameters on FSAM specimens.

Table 8. Random Forest parameter importance.

Input Parameter	VHN Importance (%)	TS Importance (%)	Rank
RPM	48.0	42.0	1
SPEED	32.0	35.0	2
TA	20.0	23.0	3

shows the importance of each parameter on VHN and TS.

3.3.3. Consistency of Feature Importance Results

A direct comparison of Pearson’s Correlation Coefficient and Random Forest importance was made to establish transparency and consistency of the results generated. Both methodologies identified the RPM as the main process parameter influencing VHN and TS. This dual confirmation validates the key finding that RPM is the most impactful factor for optimizing the process.

3.4. Correlation Coefficients (r)

Figure 7 represents the statistical analysis of the input parameters (RPM, SPEED, and TA) on the output parameters (VHN and TS). The RPM shows the highest positive correlation between VHN (r = 0.65) and TS (r = 0.55). This indicates that an increasing RPM tends to increase VHN and TS.

Random Forest Feature Importance (%)

Figure 8 shows the non-linear and combined influence of the parameters. RPM influences the highest percentage of importance for both VHN (48.0%) and TS (42.0%), making it the most important parameter.

Table 9. Pearson Correlation Coefficient and Random Forest feature importance on VHN and TS.

Input Parameter	VHN (r)	VHN Importance (%)	TS (r)	TS Importance (%)
RPM	+0.65	48.0%	+0.55	42.0%
SPEED	−0.30	32.0%	−0.40	35.0%
TA	+0.50	20.0%	+0.25	23.0%

shows the Pearson Correlation Coefficients and Random Forest feature importance for VHN and TS.

3.5. Validation

The independent validation dataset has been expanded to seven new experimental runs. This larger dataset provides stronger evidence of the model’s generalizability to process parameter combinations outside the original training data. The table below presents the comparison between the actual measured values from these new experiments and the predicted values from the ANN model, as shown in

Table 10. Independent validation results: expanded experimental dataset.

Run	RPM	SPEED	TA	Actual VHN	Predicted VHN	Abs Error VHN	Actual TS	Predicted TS	Abs Error TS
V1	1250	75	0.5	118.0	118.5	0.5	322.5	321.0	1.5
V2	1800	55	1.5	125.1	124.0	1.1	336.8	338.0	1.2
V3	1500	45	0.8	122.5	122.2	0.3	341.0	340.5	0.5
V4	1050	50	1.8	115.5	115.8	0.3	324.5	325.2	0.7
V5	1950	80	0.2	119.9	119.5	0.4	331.0	332.0	1.0
V6	1500	70	1.0	123.0	122.8	0.2	335.8	335.5	0.3
V7	1700	60	0.5	119.5	120.1	0.6	329.1	328.0	1.1

.

Validation performance metrics:

• Mean Absolute Error (MAE) for VHN: 0.486
• Mean Absolute Error (MAE) for TS: 0.90

The consistently low errors across this expanded, independent validation set confirm the robustness and reliability of the ANN model for predicting the mechanical properties of the AA8090 alloy processed by FSAM. The bar chart shown in Figure 9 visualizes the R² performance of the model under four increasingly strenuous cross-validation methods, directly testing the model’s robustness and confirming the relative importance of the input parameters.

LOPCO (Leave-One-Parameter-Combination-Out): The moderate drop in R² (6–7%) indicates that while the model is good, predicting an entirely unseen combination is harder than predicting an unseen point within a split, confirming reasonable boundary robustness.

LOFLO-RPM (Leave-One-Factor-Level-Out): This test forces the model to predict outcomes for an entire level of RPM (e.g., 1500 rpm) without any training data. The drop in R² (24–27%) conclusively confirms that rotational speed is the single most critical factor; the model’s accuracy significantly degrades when it cannot learn the full range of this parameter.

LOFLO-TA (Leave-One-Factor-Level-Out): The minimal drop in R² (2–4%) confirms that the model can generalize well even when deprived of an entire level of the tilt angle, supporting the conclusion that tilt angle has the weakest overall influence.

3.5.1. Baseline Models and ANN Ablations

The ANN model’s superior performance was benchmarked against classic and ensemble machine learning models, as well as simpler ANN topologies, as shown in

Table 11. Baseline model and ANN ablations.

Model/Ablation	VHN R2	TS R2
Current ANN (2 Hidden Layers)	0.940	0.920
Linear Regression (LR)	0.600	0.550
Random Forest (RF)	0.900	0.870
XGBoost	0.910	0.880
Simpler ANN (2 Hidden Layers)	0.850	0.800

.

The results show that the current ANN model structure yields the highest predictive accuracy for this topology.

The Simpler ANN (3-4-4-2) was used as the baseline on the architecture ablation as a way of understanding how model capacity affects predictive performance, even though the same training conditions were used. Both architectures have two hidden layers, but the Current ANN (3-6-6-2) has additional neurons and parameters to be trained, which have more capacity to model the non-linear interactions between the RPM, SPEED, TA and the outputs (VHN, TS). Table 11 reveals that the Current ANN has higher values of R², meaning that moderate model complexity is needed to estimate the latent process–property correlations. The difference in controlled performances testifies to the fact that the chosen 3 6 6 2 architecture provides optimal predictive accuracy and generalization without overfitting and is not arbitrary.

3.5.2. Input Ablation Analysis

To quantitatively assess the sensitivity of the model, input ablation analysis was performed on the removal of each input parameter to provide a strong indication of feature importance, as mentioned in the article by K. Adiga et al. [15]. The largest drop in R² occurs when RPM is excluded, confirming RPM’s major influence.

3.5.3. Residual Diagnostics and Uncertainty Estimates

The residual plot of residual diagnostics showed a random scatter pattern, confirming the model’s uniform error variance and a lack of systemic bias. To determine the uncertainty estimate, the model was enhanced using Bootstrap Aggregating (also called bootstrapping). It provided a 95% confidence interval for VHN and TS predictions, which measures the uncertainty around each point estimate.

3.6. Grouped Cross-Validation (CV) for Robustness

Grouped CV methods were used to test the model’s robustness and extrapolation capability, particularly crucial when dealing with sparse experimental data, as stated by M. S. Dahiya et al. [34].

Table 12. R² values of VHN and TS for various validation models.

Method	VHN R2	TS R2
Standard 5-Fold CV	0.940	0.920
Leave-One-Parameter-Combination-Out (LOPCO)	0.880	0.850
Leave-One-Factor-Level-Out (LOFLO-RPM)	0.700	0.650
Leave-One-Factor-Level-Out (LOFLO-TA)	0.900	0.880

shows the R² values of VHN and TS for various validation models.

3.7. Explainable AI (XAI) Techniques

Permutation Importance (PI) and Partial Dependence (PD) plots were used to independently verify the RF feature importance analysis, as mentioned in M. Akbari et al. [35] and S. Kilic et al. [36]. Permutation importance was used as an independent check on the RF feature analysis. It confirms that RPM has the highest permutation importance score for both VHN and TS. Partial Dependence (PD) plots were generated for all three inputs. These plots illustrate the minor effect of each input on the response. It shows the strong, non-linear relationship of RPM on both VHN and TS. It provides a clear, combined analysis with the RF and correlation results.

3.8. Triplicate Repeats for Experimental Noise Quantification

For separating the model error from inherent noise, triplicate experiments were made at two distinct settings to quantify the variability, as determined in the work of S. Kilic et al. [36] and shown in

Table 13. Triplicate repeats.

Setting	VHN (Mean ± SD)	TS (Mean ± SD)
Optimal TS (R = 2000, S = 45, T = 2)	117.1 ± 0.35	343.2 ± 0.76
Edge VHN (R = 1000, S = 85, T = 0)	113.0 ± 0.50	316.0 ± 0.50

. The low SD values authenticate the quality and repeatability of the experimental measurements.

3.9. Mid-Level Runs to Test Interpolation

The experimental data were generated using a Central Composite Design (CCD) involving three continuous factors. The design included factorial points defining the boundaries of the parameter space, axial points generated by varying one factor at a time around the center, and center-point runs to assess model stability. Intermediate values reported in the run table correspond to axial and center points inherent to the CCD structure. Mid-level runs (M1–M3) were specifically used to evaluate the interpolation capability of the ANN, shown by the close agreement between predicted and experimental VHN and TS values, as evidenced by S. Kilic et al. [36] and shown in

Table 14. Interpolation accuracy of the model at mid-level parameters.

Run	Actual VHN	Predicted VHN	Actual TS	Predicted TS
M1 (1250, 60, 1.0)	120.8	120.5	334.5	335.0
M2 (1750, 50, 1.5)	124.5	125.0	340.0	339.5
M3 (1500, 75, 0.5)	117.6	118.0	328.5	329.0

.

The bar chart shown in Figure 10 compares the actual measured values and the predicted values from the ANN model for M1, M2, and M3, conducted at mid-level parameters. The output responses are simultaneously compared by using two Y-axes: VHN (left side, blue bars) and TS (right side, red bars). The actual bar and predicted bar are closely aligned for every run and response. This shows the visual confirmation of the model’s accuracy. The high accuracy of the model proves that the model has learned the implicit relationship between the input and output parameters, demonstrating an excellent interpolation capability. The low absolute errors (0.3 and 1.5) quantify the model’s reliability for process control and optimization.

Figure 11 and Figure 12 show the model’s behavior by comparing the experimental and predicted values for hardness and tensile strength by run number. The final predicted average values for VHN and TS were 121.66 VHN and 329.66 MPa, respectively. The process parameters corresponding to the maximum and minimum errors were identified as 1500 rpm, 65 mm/min, 1° for VHN and 2000 rpm, 65 mm/min, and 1° for TS.

One of the major limitations observed in the work is a sudden spike and dip in the model behavior. The possible reasons for the sudden spike/dip can be attributed to the following:

i.

The current work does not consider the effect of other process parameters, such as axial force and tool geometry. The axial force and tool geometry also account for heat generation and material flow. This affects the VHN and TS of the specimens.

ii.

As RPM was found to be the most influential parameter, any vibrations that might occur in the FSAM machine during the process can lead to this spike/dip, thus making RPM the potential outlier.

4. Conclusions

The model showed evidence of stable and excellent predictive performance, confirmed by 5-fold cross-validation, reporting a mean R² of 0.940 ± 0.015 for VHN and 0.920 ± 0.020 for TS. The MAE, RMSE, and R² errors were found to be 1.0, 2.0, and 0.939 for VHN and 1.0, 2.0, and 0.919 for TS. The validation test carried out for seven new combinations of process parameters showed low, consistent errors, proving the model’s capability to predict new combinations of process parameters. RPM has been identified as the single most dominant process parameter, with its removal causing a severe drop in model accuracy (up to 27% loss in R²). The PI and PD analysis showed that RPM has the highest PI score for VHN and TS. The spike/dip in the plot between experimental and predicted values can be attributed to vibrations in the machine occurring during the process. This proves RPM is a potential outlier in the system. The mid-level runs to test the interpolation showed that the model learned the implicit relationship between input and output parameters. The average predicted values for microhardness and tensile strength were 121.66 VHN and 329.66 MPa, respectively.

The current model is limited to only three process parameters. Future work can include other parameters such as tool geometry, axial force, preheating and cooling of the material, and the number of passes. These parameters significantly affect the properties of the FSAM-built parts, and they are among the future areas of work that can be carried out. Additionally, yield strength, fatigue analysis, % elongation, and surface roughness are some of the other output parameters that can be investigated.