Modeling and Optimization for Piercing Efficiency and Energy Consumption Based on Mean Value Substaged KELM-PLS and GA Method

Table 1

Modeling variable table for piercing efficiency and energy.

Number	Original; variables	The first stage variables		The second stage variables		The third stage variables		The mean of variables
		Efficiency	Energy consumption	Efficiency	Energy consumption	Efficiency	Energy consumption
1	𝑥1	𝑥1,1	𝑥1,1	𝑥2,1	𝑥2,1	𝑥3,1	𝑥3,1	The percent reduction of upper roll
2	𝑥2	𝑥1,2	𝑥1,2	𝑥2,2	𝑥2,2	𝑥3,2	𝑥3,2	The percent reduction of under roll
3	𝑥3	𝑥1,3	𝑥1,3	𝑥2,3	𝑥2,3	𝑥3,3	𝑥3,3	The angle of inclination of upper roll
4	𝑥4	𝑥1,4	𝑥1,4	𝑥2,4	𝑥2,4	𝑥3,4	𝑥3,4	The angle of inclination of under roll
5	𝑥5	𝑥1,5	𝑥1,5	𝑥2,5	𝑥2,5	𝑥3,5	𝑥3,5	The rotational speed of upper roll
6	𝑥6	𝑥1,6	𝑥1,6	𝑥2,6	𝑥2,6	𝑥3,6	𝑥3,6	The rotational speed of under roll
7	𝑥7	𝑥1,7						The position change range of pusher
8	𝑥8	𝑥1,8						The actual position of mandrel thrust block
9	𝑥9	𝑥1,9		𝑥2,7		𝑥3,7		The position of mandrel
10	𝑥10			𝑥2,8	𝑥2,7	𝑥3,8	𝑥3,7	The rotational speed of left guide disc
11	𝑥11			𝑥2,9	𝑥2,8	𝑥3,9	𝑥3,8	The rotational speed of left guide disc
12	𝑥12			𝑥2,10	𝑥2,9			The temperature of tube blank