Multi-objective optimization of the process combining ultrasonic vibration and age-forming of dissimilar friction-stir-welded Aluminium T-stiffened plates

Open Access

Table 4

Linear regression models for Y₁′, Y₂′ and Y₃′.

Type	Regression equations
Inverse forming rate	$\begin{array}{l} Y_{1}^{'} = 0.015 x_{1}^{2} + 0.534 x_{2}^{2} + 0.255 x_{3}^{2} + 0.016 x_{1} x_{2} + 0.023 x_{1} x_{3} \\ + 0.248 x_{2} x_{3} - 5.853 x_{1} - 16.344 x_{2} - 13.461 x_{3} + 809.782 \end{array}$
Inverse tensile strength	$\begin{array}{l} Y_{2}^{'} = 0.22 x_{1}^{2} + 4.56 x_{2}^{2} + 2.16 x_{3}^{2} + 0.77 x_{1} x_{2} + 0.38 x_{2} x_{3} - 77.54 x_{1} \\ - 209.58 x_{2} - 56.6 x_{3} + 9721.88 \end{array}$
Inverse elongation	$\begin{array}{l} Y_{3}^{'} = 0.19 x_{1}^{2} + 10.82 x_{2}^{2} - 6.6 x_{3}^{2} + 0.16 x_{1} x_{2} + 0.26 x_{1} x_{3} + 6.53 x_{2} x_{3} \\ - 65.8 x_{1} - 288.17 x_{2} - 60.18 x_{3} + 7450.76 \end{array}$

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