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

Table 1

Cost of KPLS, RKPLS, and DRKPLS with adaptive model.

Method	Iterations	Cost
KPLS	Initialize training data ,	O (2)
	Calculate the matrix of kernel K and scale it using equation (9)	O
	Calculate the number of LVs
	Calculate the SPE limit	O (1)
	Obtain the new observation	O (1)
	Compute the kernel vector	O (N)
	Calculate the estimated output , using equation (15)	O (1)
	Evaluate SPE index	O (1)
	Total:
RKPLS	Initialize training data ,	O (2)
	Calculate the matrix of kernel K and scale it using equation (22)	O
	Compute the reduced number of LVs	O
	Calculate the SPE limit	O (1)
	Obtain the new observation	O (1)
	Compute the vector of kernel	O (r)
	Calculate the estimated output	O (1)
	Evaluate SPE index	O (1)
	Total:
DRKPLS	Initialize training data ,	O (2)
	Compute the matrix of kernel K and scale it using equation (24)	O
	Compute the reduced number of LVs	O
	Calculate the SPE limit	O (1)
	Obtain the new observation	O (1)
	Calculate the kernel vector	O (r)
	Update kernel matrix	O
		O (1)
	If the condition is satisfied	O
	If the condition presented by equation (20)	O
	Update the LVs number	O
	Evaluate SPE index	O (1)
	Total: