Partial PCA based on principal component analysis (PCA) with ideas borrowed from parity relations is a useful method in fault isolation (J. Gertler, W. Li, Y. Huang, T.J. McAvoy, Isolation enhanced principal component analysis, AIChE Journal 45(2) (1999) 323-334). By performing PCA on subsets of variables, a set of structured residuals can be obtained in the same way as structured parity relations. The structured residuals are utilized in composing an isolation scheme for sensor and actuator faults, according to a properly designed incidence matrix. To overcome the limitations of PCA, nonlinear approaches based on generalized PCA (GPCA) and nonlinear PCA (NPCA) are proposed. The nonlinear methods are demonstrated on an artificial 2x2 system while simulation studies on the Tennessee Eastman process illustrate the linear method and some extensions. (C) 2000 Elsevier Science Ltd. All rights reserved.