Quality-Related Process Monitoring Based on Total Kernel PLS Model and Its Industrial Application

Algorithm 3

KPLS algorithm.

(1) Set 𝑖=1, initialize 𝐮_𝑖 as the first column of 𝐘_𝑖.

(2) 𝐭_𝑖=Φ_𝑖𝐰_𝑖=𝐊_𝑖𝐮_𝑖, where 𝐰_𝑖=Φ^𝑇_𝑖𝐮_𝑖.

(3) Scale 𝐭_𝑖 to unit length, 𝐭_𝑖=𝐭_𝑖/𝐭_𝑖.

(4) 𝐮_𝑖=𝐘_𝑖𝐪_𝑖, where 𝐪_𝑖=𝐘^𝑇_𝑖𝐭_𝑖.

(5) Scale 𝐮_𝑖 to unit length, 𝐮_𝑖=𝐮_𝑖/𝐮_𝑖.

Repeat (2)–(5) until 𝐭_𝑖 convergence.

(6) Deflate matrices 𝐊, 𝐘 and Φ:

  Φ_𝑖+1=𝐈−𝐭_𝑖𝐭^𝑇_𝑖Φ_𝑖, 𝐘_𝑖+1=𝐈−𝐭_𝑖𝐭^𝑇_𝑖𝐘_𝑖

     𝐊_𝑖+1=𝐈−𝐭_𝑖𝐭^𝑇_𝑖𝐊_𝑖𝐈−𝐭_𝑖𝐭^𝑇_𝑖.

(7) Set 𝑖=𝑖+1, loop to step (1), until 𝑖>𝐴.