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

Algorithm 1

T-KPLS algorithm for comprehension.

(1) Perform KPLS algorithm on 𝐗 and 𝐘 to get the model described in (3)

(2) Run PCA on 𝐘 with 𝐴_𝑦 components, where 𝐘=𝐓_𝑦𝐐^𝑇_𝑦, 𝐴_𝑦=rank(𝐐)

(3) Define Φ_𝑦=𝐓_𝑦𝐏^𝑇_𝑦, where 𝐏^𝑇_𝑦=𝐓^𝑇_𝑦𝐓_𝑦⁻¹𝐓^𝑇_𝑦Φ, 𝐏_𝑦∈ℜ^{𝑀×𝐴𝑦}

(4) Run PCA on Φ_𝑜=Φ−Φ_𝑦, with 𝐴_𝑜 components, 𝐴_𝑜=𝐴−𝐴_𝑦, Φ_𝑜=𝐓_𝑜𝐏^𝑇_𝑜

(5) Perform PCA on Φ_𝑟, with 𝐴_𝑟 components, where 𝐴_𝑟 is determined using PCA methods,

   Φ_𝑟𝑝=𝐓_𝑟𝐏^𝑇_𝑟

(6) Φ_𝑟𝑟=Φ_𝑟−Φ_𝑟𝑝=Φ_𝑟−𝐓_𝑟𝐏^𝑇_𝑟