To handle the nonlinear problem for process monitoring

a new technique based on kernel partial least squares(KPLS)is developed.KPLS is an improved partial least squares(PLS)method

and its main idea is to first map the input space into a high-dimensional feature space via a nonlinear kernel function and then to use the standard PLS in that feature space.Compared to linear PLS

KPLS can make full use of the sample space information

and effectively capture the nonlinear relationship between input variables and output variables.Different from other nonlinear PLS

KPLS requires only linear algebra and does not involve any nonlinear optimization.For process data

firstly KPLS was used to derive regression model and got the score vectors

and then two statistics

T2 and SPE

and corresponding control limits were calculated.A case study of the Tennessee-Eastman(TE)process illustrated that the proposed approach showed superior process monitoring performance compared to linear PLS.