Table 7 Significant factors identified from the physical and statistical perspectives.

From: Factorial design analytics on effects of material parameter uncertainties in multiphysics modeling of additive manufacturing

Perspective

Physical

Statistical

Results

Physical phenomena such as the marangoni effect, effective energy input, and heat transport mechanisms significantly influence melt pool geometry. It is universally agreed in the AM community that the laser power absorption exhibits a dominating influence on the melt pool dimensions. The crucial physical parameters based on the aforementioned domain knowledge are summarized as follows:

• \(Pr=\frac{{c}_{p}\mu }{\lambda }\)

• \(Ma=-\frac{d\gamma }{dT}\frac{w{{\Delta }}T}{\mu \alpha }\)

• \(Pe=\frac{UL}{\alpha }\)

• \(Re=\frac{Pe}{Pr}\)

• η

• μ

• − dγ/dT

• Data visualization via Figs. 1, 2, 3 consistently identify PA as a dominating factor with the largest uncertainty, and suspect the significance of some 2-factor interactions.

• Both variable selection methods (best subset selection and LASSO regression) identify PA, λ, μ, \(\lambda \,* \, -{\rm{d}}\gamma/{\rm{dT}}\), \({P}_{A}\,*\, \mu\), \(\lambda \, *\, \mu\), \({P}_{A}\,*\, \mu \, *\, - \,{\rm{d}}\gamma/{\rm{Td}}\), \({P}_{A}\,*\, \lambda\,*\gamma\,*\, -\,{\rm{d}}\gamma/{\rm{dT}}\), \(\lambda \, * \, \mu\, *\, \gamma\, *\, - \,{\rm{d}}\gamma/{\rm{dT}}\), as statistically significant variables.

• The LASSO model achieves the best bias-variance tradeoff. The corresponding parameter ranking of significant main effects and 2-factor interactions from the optimal LASSO model in descending order is as follows: PA, λ, μ, \(\lambda\, *\,-\, {\rm{d}}\gamma/{\rm{dT}}\), \({P}_{A}\,*\, \mu\), \(\lambda \,* \,\mu\), \(\lambda\,*\,\gamma\), \({P}_{A}\,*\,-\,{\rm{d}}\gamma/{\rm{dT}}\), \({P}_{A}\, *\,\gamma\).

Interpretation

• Factors PA, λ, μ, − dγ/dT are significant

• Suspected significant interactions: \(\lambda\,*\,\mu,\,\lambda\,*\, -\,{\rm{d}}/{\rm{dT}},\,\mu\,*\,{\rm{d}}\gamma/{\rm{dT}},\,\lambda\,*\,\mu\,*\,-\,{\rm{d}}\gamma/{\rm{dT}}\)

• Factors PA, λ, μ are significant.

• Confirmed significant interactions: \(\lambda\, *\, \mu, \, \lambda\,*\,\gamma,\,\lambda\,*\,-\,{\rm{d}}\gamma/{\rm{dT}},\,{P}_{A}\,*\,\mu\)

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