Multiple operating modes and complex data distributions are common in modern industrial processes

so the process variable does not completely obey Gaussian distribution

and its mean and covariance structure tend to change with the switching of working conditions. In order to detect various faults in such production process timely

a novel online monitoring strategy based on locality preserving projection (LPP) and local density estimation with variable bandwidth is proposed. Firstly

LPP is introduced for feature extraction and dimension reduction

and then a variable bandwidth kernel density estimate function is adopted to compute every sample's local density factor

which is used as a monitoring statistic value. Finally

the results of numerical examples and TE chemical process simulation experiment validate the effectiveness and utility of the proposed method for the fault detection of multi-mode processes.