A probabilistic kernel principal component analysis mixture model (PKPCAM) based on Bayesian inference was proposed to detect and diagnose the fault in the nonlinear and multimode processes. In PKPCAM

each operating mode was characterized by a local probabilistic kernel principal component

leading to a series of components corresponding to multiple operation conditions. Firstly

process data were projected from the original measurement space into the high-dimensional feature space. Then the probabilistic kernel principal component analysis mixture model was estimated in the feature space and used to characterize the multiple local components from the viewpoint of probability. Finally

utilizing the posterior probability of the monitored sample in kernel subspace

according to Mahalanobis distance within the local mode

the Bayesian reference based global probability index was proposed for fault detection. And meantime

using the relative contribution of variable within mode

global contribution index was derived to perform diagnosis. Comparing to the two methods based on the sub-principal component analysis using k-means clustering and the kernel principal component analysis

the feasibility and effectiveness by the proposed Bayesian inference based PKPCAM method for fault detection and diagnosis in nonlinear and multimode process was validated on Tennessee Eastman process.