Page 65 - MSAM-4-3

Materials Science in Additive Manufacturing Bead geometry prediction in laser-arc AM

visualization. The study began by calculating SHAP values 3. Results and discussion
for every feature, thereby quantifying their influence on
the predictions; the original features were then contrasted In this study, the validity of the proposed PSO-EP method
with newly derived ones to confirm the performance was demonstrated. For performance evaluation, the
gains attributable to the new attributes. Subsequently, the PSO-EP’s predictions were initially benchmarked against
SHAP visualization toolkit was employed to depict feature each single base model to measure gains in prediction
importance and the directionality of their effects, affording precision. Subsequently, it was assessed alongside
a deeper dissection of the model’s reasoning process. other widely used ensemble forecasting approaches to
underscore the PSO-EP’s overall superiority. Finally,
2.5. Parameter setting of the PSO-EP an importance analysis of the process parameters was
conducted to uncover their individual impacts on the
The training set trained multiple regression models, while prediction outcomes.
five-fold cross-validation on the validation set tuned their
hyperparameters. Once tuning was completed, the model 3.1. Comparison of PSO-EP with base models
with the best validation performance was chosen to forecast
bead size on the test set; these forecasts constituted the To assess the superiority of PSO-EP, the present study
response values. Next, the response values together with conducted a comparison against four baseline models:
the models’ evaluation indices were fed into the ensemble GPR, SVR, ANN, and ELM. Figures 7 and 8 illustrate the
module, which used the metric of Equation II as a fitness performance of the models in the prediction tasks for weld
function and applied PSO to derive a weighted fusion bead width and height, respectively. To facilitate a clear
of the individual outputs. Within the PSO-EP method, comparison, the figures display only the test set predictions
the weight-assignment stage employed up to 50,000 along with their respective error curves.
iterations and a swarm of 200 particles. Iterative search Figure 7 illustrates that PSO-EP excels in weld
ultimately yielded the optimal set of model weights, and bead width prediction, with an R of 0.9567, markedly
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a consolidated estimate of bead dimensions was output. outperforming GPR, SVR, ANN, and ELM, which signifies
The PSO-EP approach was further benchmarked against its enhanced capability to accurately capture the overall
various alternative techniques to evaluate its efficacy. width variation trend; simultaneously, PSO-EP records the
smallest RMSE and MAE values, substantiating its lowest
2.6. Model evaluation indicators overall prediction error and MAE (Table 7). Nevertheless,
Once the prediction was complete, the model’s the highest relative error observed in extreme samples is
performance was assessed by computing the error between 5.6%, which is only superior to ANN’s 7.8%, indicating
the true values and the predicted results for the test data. potential for further enhancement in limiting the
Smaller errors indicated better model performance. For maximum error. Sample 6 showed a comparatively
the regression problem concerning the LAHAM weld bead large error in weld bead width prediction. The feature
width and height, this study used mean absolute error importance analysis in section 3.3 indicated that wire feed
(MAE), root mean squared error (RMSE), and coefficient speed and welding speed are the key factors determining
of determination (R ) as performance metrics. MAE and width; for this sample, the wire feed speed was 7.80 m/min
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RMSE assess the deviation between predicted and actual and the welding speed was 510 mm/min. Figure 9 reveals
values, with RMSE being more sensitive to larger errors. that this set of parameters is positioned at the boundary
R reflects the model’s ability to explain the variability in of the process window, where their interaction drives an
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the data, with values closer to 1 indicating a better fit. A increase in bead width, resulting in an overestimation by
comprehensive evaluation of model performance can be the model and a magnified error. This finding suggests,
achieved by integrating these metrics. first, that the model’s generalization at the boundary of
the parameter space can be further enhanced; second, that
1 n  because this condition approaches the experimental limit,
MAE | y y | (VII)
n i1 i i sporadic experimental inaccuracies could also exacerbate
the prediction error.
1 n Regarding weld bead height prediction (Figure 8),
RMSE = ∑ (y − y 2
ˆ )
n i= 1 i i (VIII) while all models display comparable overall trend curves,
PSO-EP notably excels in fitting regions with pronounced
i ∑ ( y − y ) 2 height fluctuations, where its predicted curve almost
ˆ
R = 1− i i (IX) perfectly overlaps with observed values; by comparison,
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i ∑ ( y − ) y 2 GPR, SVR, ANN, and ELM show evident discrepancies at
i
Volume 4 Issue 3 (2025) 8 doi: 10.36922/MSAM025220036