Improved Dynamic Optimized Kernel Partial Least Squares for Nonlinear Process Fault Detection

Algorithm 2

DRKPLS algorithm.

Offline phase:
(1)	Initialize
The initial data X and Y
The reduced set of data
The SPE index of reduced observations
The number of LVs and the reduced Gram matrix
Online phase:
(2)	;
(3)	Acquire a new observation ;
(4)	Calculate the SPE index using equation (25);
(5)	If is satisfied, then go to step 6; otherwise, return to step 2;
(6)	If the condition presented by equation (20) is satisfied, then go to step 7. Otherwise, return to step 2;
(7)	Update the matrix of reduced data;
(8)	Update the reduced Gram matrix;
(9)	Update the SPE index;
(10)	Update the LVs and return to step 2;